ENCYCLOPEDIA OF TRIANGLE CENTERS

PART 5

X(801)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (csc A)/(cos²B + cos²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (csc A)/(cos²B + cos²C)

X(801) lies on these lines: 4,1092   10,775
X(801) = isogonal conjugate of X(800)

X(802) = ODD (- 2, 1) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-3(b¹ - c¹) + a⁰(b^-2 - c^-2)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(802) lies on the line at infinity.
X(802) lies on this line: 30,511
X(802) = isogonal conjugate of X(803)

X(803) = o-(- 2, 1) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-3(b¹ - c¹) + a⁰(b^-2 - c^-2)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(803) lies on the circumcircle.
X(803) = isogonal conjugate of X(802)

X(804) = ODD (- 2, 2) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-3(b² - c²) + a¹(b^-2 - c^-2)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(804) lies on the line at infinity.
X(804) lies on these lines: 2,351   30,511   98,878   99,670   115,1084   147,684   669,850
X(804) = isogonal conjugate of X(805)

X(805) = o-(- 2, 2) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-3(b² - c²) + a¹(b^-2 - c^-2)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(805) lies on the circumcircle.
X(805) lies on these lines: 98,385   99,512   110,669   111,694   187,729   249,827   574,843   691,882   888,892
X(805) = isogonal conjugate of X(804)

X(806) = ODD (- 2, 3) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-3(b³ - c³) + a²(b^-2 - c^-2)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(806) lies on the line at infinity.
X(806) lies on this line: 30,511
X(806) = isogonal conjugate of X(807)

X(807) = o-(- 2, 3) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-3(b³ - c³) + a²(b^-2 - c^-2)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(807) lies on the circumcircle.
X(807) = isogonal conjugate of X(806)

X(808) = ODD (- 2, 4) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-3(b⁴ - c⁴) + a³(b^-2 - c^-2)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(808) lies on the line at infinity.
X(808) lies on this line: 30,511
X(808) = isogonal conjugate of X(809)

X(809) = o-(- 2, 4) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-3(b⁴ - c⁴) + a³(b^-2 - c^-2)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(809) lies on the circumcircle.
X(809) = isogonal conjugate of X(808)

X(810)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin 2A (cos²B - cos²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin²A cos A (cos²B - cos²C)
X(810) lies on these lines: 521,656   661,663   667,788
X(810) = isogonal conjugate of X(811)

X(811)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (csc 2A)/(cos²B - cos²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sec A)/(cos²B - cos²C)
X(811) lies on these lines: 1,336   75,1099   99,108   112,789   162,799   350,447   645,648   662,823
X(811) = isogonal conjugate of X(810)

X(812) = ODD (- 1, 1) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-2(b¹ - c¹) + a⁰(b^-1 - c^-1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(812) lies on the line at infinity.
X(812) lies on these lines: 30,511   190,646   649,693   673,1024   903,1022   1015,1086
X(812) = isogonal conjugate of X(813)

X(813) = o-(- 1, 1) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-2(b¹ - c¹) + a⁰(b^-1 - c^-1)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(813) lies on the circumcircle.
X(813) lies on these lines:
99,1016   100,649   101,667   103,295   105,238   106,292   163,827   190,789   334,767   335,675   644,932   689,799   692,825   739,902   765,798   898,1023   927,1025
X(813) = isogonal conjugate of X(812)

X(814) = ODD (- 1, 2) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-2(b² - c²) + a¹(b^-1 - c^-1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(814) lies on the line at infinity.
X(814) lies on this line: 30,511
X(814) = isogonal conjugate of X(815)

X(815) = o-(- 1, 2) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-2(b² - c²) + a¹(b^-1 - c^-1)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(815) lies on the circumcircle.
X(815) = isogonal conjugate of X(814)

X(816) = ODD (- 1, 3) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-2(b³ - c³) + a²(b^-1 - c^-1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(816) lies on the line at infinity.
X(816) lies on this line: 30,511
X(816) = isogonal conjugate of X(817)

X(817) = o-(- 1, 3) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-2(b³ - c³) + a²(b^-1 - c^-1)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(817) lies on the circumcircle.
X(817) = isogonal conjugate of X(816)

X(818) = ODD (- 1, 4) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-2(b⁴ - c⁴) + a³(b^-1 - c^-1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(818) lies on the line at infinity.
X(818) lies on this line: 30,511
X(818) = isogonal conjugate of X(819)

X(819) = o-(- 1, 4) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-2(b⁴ - c⁴) + a³(b^-1 - c^-1)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(819) lies on the circumcircle.
X(819) = isogonal conjugate of X(818)

X(820)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos²A (cos²B + cos²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = cos A cos²A (cos²B + cos²C)
X(820) lies on these lines: 1,29   3,296   662,775   836,1100
X(820) = isogonal conjugate of X(821)

X(821)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec²A /(cos²B + cos²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(821) lies on these lines: 158,255   243,411   774,823
X(821) = isogonal conjugate of X(820)

X(822)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec²B - sec²C
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A (sec²B - sec²C)
X(822) lies on this line: 44,513
X(822) = isogonal conjugate of X(823)

X(823)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(sec²B - sec²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(823) lies on these lines: 100,107   110,681   158,897   264,379   648,651   662,811   774,821
X(823) = isogonal conjugate of X(822)

X(824) = ODD (0, 3) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-1(b³ - c³) + a²(b⁰ - c⁰)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(824) lies on the line at infinity.
X(824) lies on these lines: 30,511   321,693
X(824) = isogonal conjugate of X(825)

X(825) = o-(0, 3) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-1(b³ - c³) + a²(b⁰ - c⁰)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(825) lies on the circumcircle.
X(825) lies on these lines:
1,761   6,753   31,743   32,731   99,163   103,572   105,985   560,717   692,813   767,870
X(825) = isogonal conjugate of X(824)

X(826) = ODD (0, 4) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a^-1(b⁴ - c⁴) + a³(b⁰ - c⁰)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(826) lies on the line at infinity.
X(826) lies on this line: 30,511   54,879   76,882
X(826) = isogonal conjugate of X(827)

X(827) = o-(0, 4) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a^-1(b⁴ - c⁴) + a³(b⁰ - c⁰)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(827) lies on the circumcircle.
X(827) lies on these lines:
5,83   6,755   31,745   32,733   82,759   111,251   163,813   249,805   250,935   560,719   662,831   741,849
X(827) = isogonal conjugate of X(826)

X(828)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin C sec²B + sin B sec²C
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
X(828) = isogonal conjugate of X(829)

X(829)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(sin C sec²B + sin B sec²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(829) = isogonal conjugate of X(828)

X(830) = ODD (1, 3) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a⁰(b³ - c³) + a²(b¹ - c¹)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(830) lies on the line at infinity.
X(830) lies on this line: 30,511
X(830) = isogonal conjugate of X(831)

X(831) = o-(1, 3) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a⁰(b³ - c³) + a²(b¹ - c¹)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(831) lies on the circumcircle.
X(831) lies on this line: 662,827
X(831) = isogonal conjugate of X(830)

X(832) = ODD (1, 4) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a⁰(b⁴ - c⁴) + a³(b¹ - c¹)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(832) lies on the line at infinity.
X(832) lies on these lines: 30,511   656,667
X(832) = isogonal conjugate of X(833)

X(833) = o-(1, 4) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a⁰(b⁴ - c⁴) + a³(b¹ - c¹)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(833) lies on the circumcircle.
X(833) lies on these lines: 106,977   759,1010
X(833) = isogonal conjugate of X(832)

X(834) = ODD (2, 3) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a¹(b³ - c³) + a²(b² - c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(834) lies on the line at infinity.
X(834) lies on this line: 30,511
X(834) = isogonal conjugate of X(835)

X(835) = o-(2, 3) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a¹(b³ - c³) + a²(b² - c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(835) lies on the circumcircle.
X(835) lies on these lines: 110,190   335,741
X(835) = isogonal conjugate of X(834)

X(836)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin B sec²B + sin C sec²C
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
X(836) lies on these lines: 1,393   37,73   820,1100
X(836) = isogonal conjugate of X(837)

X(837)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(sin B sec²B + sin C sec²C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(837) lies on this line: 393,394
X(837) = isogonal conjugate of X(836)

X(838) = ODD (3, 4) INFINITY POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a²(b⁴ - c⁴) + a³(b³ - c³)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(838) lies on the line at infinity.
X(838) lies on this line: 30,511
X(838) = isogonal conjugate of X(839)

X(839) = o-(3, 4) CIRCUMCIRCLE POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a²(b⁴ - c⁴) + a³(b³ - c³)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(839) lies on the circumcircle.
X(839) lies on these lines: 110,668   334,741
X(839) = isogonal conjugate of X(838)

X(840) = ISOGONAL CONJUGATE of X(528)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(2ax - by - cz), x = x(A,B,C) = 1 - cos(B - C)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(840) lies on the circumcircle.
X(840) lies on these lines: 6,919   7,927   36,101   55,901   100,518   105,513   106,663   109,902   759,1019   898,1083
X(840) = isogonal conjugate of X(528)

X(841) = ISOGONAL CONJUGATE of X(541)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(2ax - by - cz), x = x(A,B,C) = 1/(cos A - 2 cos B cos C)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(841) lies on the circumcircle.
X(841) lies on this line: 376,476
X(841) = isogonal conjugate of X(541)

X(842) = ISOGONAL CONJUGATE of X(542)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(2ax - by - cz), x = x(A,B,C) = sec(A + ω)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(842) lies on the circumcircle.
X(842) lies on these lines: 2,476   3,691   4,935   23,110   30,99   74,512   98,523   107,468   111,647   112,186   858,925
X(842) = isogonal conjugate of X(542)

X(843) = ISOGONAL CONJUGATE of X(543)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(2ax - by - cz), x = x(a,b,c) = bc/(b² - c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(843) lies on the circumcircle.
X(843) lies on these lines: 6,691   99,525   110,187   111,512   574,805
X(843) = isogonal conjugate of X(543)

X(844)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = - x + y + z, x = x(A,B,C) = sin(A/2) sec²(A/2)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #2768, May 3, 2001.
X(844) lies on these lines: 166,167   173,503

X(845)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = - x + y + z, x = x(A,B,C) = sin²(A/2) sec(A/2)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #2768, May 3, 2001.
X(845) lies on these lines: 164,362   165,166   173,503

X(846)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = - a² + b² + c² + bc + ca + ab
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a f(a,b,c)
This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #3001, June 11, 2001.
X(846) lies on these lines: 1,21   2,1054   6,1051   9,43   35,228   37,171   55,984   100,756   333,740   405,986   982,1001

X(847)
Trilinears        sec A sec 2A : sec B sec 2B : sec C sec 2C
Barycentrics  tan A sec 2A : tan B sec 2B : tan C sec 2C
This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #3130, June 25, 2001; see also Jean-Pierre Ehrmann, #3135, June 26, 2001. The problem and solution may be stated as follows. Let ABC be a triangle, L_a, L_b, L_c the perpendicular bisectors of sides BC, CA, AB, and AA', BB', CC' the altitudes of ABC, respectively. Let A_b be the point of intersection of AA' and L_b, and let A_c be the point of intersection of AA' and L_c. Let A" be the point of intersection of BA_b and CA_c. Define B" and C" cyclically. Then triangle A"B"C" is perspective to triangle ABC, with perspector X(847).
X(847) lies on these lines: 2,254   3,925   4,52   24,96   91,225   378,1105   403,1093

X(848)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (csc A)/(cot A - cot A'), where A' = 2πa/(a + b + c)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 1/(cot A - cot A'), A' = 2πa/(a + b + c)
X(848) point is introduced by Paul Yiu in Hyacinthos #2704, April 7, 2001 (see also #2708, April 10, 2001) as the solution X of the equation
angle BXC : angle CXA : angle AXB = a : b : c.

X(849)
Trilinears        [a/(b + c)]² : [b/(c + a)]² : [c/(a + b)]²
Barycentrics  a[a/(b + c)]² : b[b/(c + a)]² : c[c/(a + b)]²
Let D denote the circumcircle of triangle ABC. Let D_A be the circle tangent to sideline BC and tangent to D at A. Define D_B and D_C cyclically. Let E_A and F_A be the points in which circles D_B and D_C meet. Define E_B, F_B and E_C, F_C cyclically. Then lines E_AF_A, E_BF_B, E_CF_C are sidelines of a triangle A'B'C' homothetic to ABC, and X(849) is the center of homothety. See A. Hatzipolakis and P. Yiu, Hyacinthos #2056-2070, December, 2000.
X(849) lies on these lines: 32,163   36,58   110,595   249,1110   741,827   757,763
X(849) = isogonal conjugate of X(1089)

X(850) = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA
Trilinears        (b² - c²)/a³ : (c² - a²)/b³ : (a² - b²)/c³
Barycentrics  (b² - c²)/a² : (c² - a²)/b² : (a² - b²)/c²
The barycentric product of X(850) and the circumcircle is the Kiepert hyperbola.
X(850) lies on these lines: 2,647   99,476   110,685   297,525   316,512   325,523   340,520   669,804   670,892
X(850) = isotomic conjugate of X(110)
X(850) = anticomplement of X(647)

X(851) = INTERCEPT OF EULER LINE AND POLE OF X(1)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin 2B sin(C - A) + sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(851) lies on these lines: 2,3   42,65   43,46   44,513   226,228

X(852) = INTERCEPT OF EULER LINE AND POLE OF X(3)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec C sin 2B sin(C - A) + sec B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(852) lies on these lines: 2,3   216,373   520,647

X(853) = INTERCEPT OF EULER LINE AND POLE OF X(55)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sec²(C/2) sin 2B sin(C - A) + sec²(B/2) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(853) lies on these lines: 2,3   657,663

X(854) = INTERCEPT OF EULER LINE AND POLE OF X(56)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = csc²(C/2) sin 2B sin(C - A) + csc²(B/2) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(854) lies on this line: 2,3

X(855) = INTERCEPT OF EULER LINE AND POLE OF X(57)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = cot(C/2) sin 2B sin(C - A) + cot(B/2) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(855) lies on these lines: 2,3   513,663

X(856) = INTERCEPT OF EULER LINE AND POLE OF X(63)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = tan C sin 2B sin(C - A) + tan B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(856) lies on these lines: 2,3   521,656

X(857) = INTERCEPT OF EULER LINE AND POLE OF X(75)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin²C sin 2B sin(C - A) + sin²B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(857) lies on these lines: 2,3   514,661
X(857) = inverse of X(379) in the orthocentroidal circle

X(858) = INTERCEPT OF EULER LINE AND POLE OF X(76)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin³C sin 2B sin(C - A) + sin³B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(858) lies on these lines: 2,3   50,230   67,524   125,511   126,625   316,691   325,523   842,925
X(858) = inverse of X(22) in the circumcircle
X(858) = inverse of X(2) in the nine-point circle
X(858) = complement of X(23)
X(858) = anticomplement of X(468)

X(859) = INTERCEPT OF EULER LINE AND POLE OF X(81)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = (sin A + sin B) sin 2B sin(C - A) + (sin A + sin C) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(859) lies on these lines: 2,3   36,238   56,58   81,957   198,284   283,945   333,956

X(860) = INTERCEPT OF EULER LINE AND POLE OF X(82)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = (tan A + tan B) sin 2B sin(C - A) + (tan A + tan C) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(860) lies on these lines: 2,3   8,1068   10,201   34,997   240,522

X(861) = INTERCEPT OF EULER LINE AND POLE OF X(9)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = tan(C/2) sin 2B sin(C - A) + tan(B/2) sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(861) lies on these lines: 2,3   650,663

X(862) = INTERCEPT OF EULER LINE AND POLE OF X(19)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = cot C sin 2B sin(C - A) + cot B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(862) lies on these lines: 2,3   661,663

X(863) = INTERCEPT OF EULER LINE AND POLE OF X(31)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = csc²C sin 2B sin(C - A) + csc²B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(863) lies on these lines: 2,3   667,788

X(864) = INTERCEPT OF EULER LINE AND POLE OF X(32)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = csc³C sin 2B sin(C - A) + csc³B sin 2C sin(B - A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(864) lies on these lines: 2,3   669,688

X(865) = INTERCEPT OF EULER LINE AND POLE OF X(512)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin 2B csc²C sin(C - A) csc(A - B) - sin 2C csc²B sin(B - A) csc(A - C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(865) lies on this line: 2,3   351,888

X(866) = INTERCEPT OF EULER LINE AND POLE OF X(513)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin 2B sin(A - C)/(sin A - sin B) - sin 2C sin(A - B)/(sin A - sin C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(866) lies on these lines: 2,3   244,665

X(867) = INTERCEPT OF EULER LINE AND POLE OF X(514)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin C sin 2B sin(A - C)/(sin A - sin B) - sin B sin 2C sin(A - B)/(sin A - sin C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(867) lies on these lines: 2,3   11,244

X(868) = INTERCEPT OF EULER LINE AND POLE OF X(523)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = sin 2B sin(A - C) csc(A - B) - sin 2C sin(A - B) csc(A - C)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(868) lies on these lines: 2,3   115,125   127,136

X(869)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²(b² + c² + bc)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(869) lies on these lines:
1,2   6,292   31,32   38,980   55,893   100,731   101,743   192,1045   210,1107
X(869) = isogonal conjugate of X(870)
X(869) = isotomic conjugate of X(871)

X(870)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a²(b² + c² + bc)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(870) lies on these lines:
1,76   2,292   6,75   34,331   56,85   58,274   86,871   106,789   767,825
X(870) = isogonal conjugate of X(869)
X(870) = isotomic conjugate of X(984)

X(871)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a⁴(b² + c² + bc)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(871) lies on these lines:
2,561   75,700   76,335   86,870   310,982   675,789
X(871) = isotomic conjugate of X(869)

X(872)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [a(b + c)]²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(872) lies on these lines:
6,292   37,42   41,560   43,75   190,1045   386,984   688,798   740,1089
X(872) = isotomic conjugate of X(873)

X(873)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [a(b + c)]^{- 2}
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(873) = isotomic conjugate of X(872)
X(873) = isotomic conjugate of X(756)
X(873) lies on these lines:
2,799   81,239   86,310   261,552   689,741

X(874)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(874) lies on these lines:
1,75   99,670   100,789   190,646
X(874) = isogonal conjugate of X(875)
X(874) = isotomic conjugate of X(876)

X(875)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(875) lies on these lines:
1,512   31,669   42,649   213,667   291,659   295,926
X(875) = isogonal conjugate of X(874)

X(876)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(1)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(876) lies on these lines:
1,512   10,514   37,513   75,523   291,891   292,659   295,928   335,900   741,759
X(876) = isogonal conjugate of X(874)

X(877)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(877) lies on these lines: 4,69   99,112
X(877) = isogonal conjugate of X(878)
X(877) = isotomic conjugate of X(879)

X(878)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(878) lies on these lines:
3,525   25,669   32,512   98,804   184,647
X(878) = isogonal conjugate of X(879)

X(879)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(879) lies on these lines:
3,525   4,512   6,523   54,826   66,924   67,526   69,520   74,98   287,895
X(879) = isotomic conjugate of X(877)

X(880)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(6)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(880) lies on these lines: 6,76   99,670   886,892
X(880) = isogonal conjugate of X(881)
X(880) = isotomic conjugate of X(882)

X(881)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(6)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(881) lies on these lines: 39,512   351,694
X(881) = isogonal conjugate of X(880)

X(882)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(6)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(882) lies on these lines:
6,688   39,512   76,826   141,523   691,805   694,888   733,755
X(882) = isotomic conjugate of X(880)

X(883)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(7)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(883) lies on these lines: 7,8   190,644
X(883) = isogonal conjugate of X(884)
X(883) = isotomic conjugate of X(885)

X(884)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(7)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(884) lies on these lines:
21,885   31,649   41,663   55,650   56,667   105,659
X(884) = isogonal conjugate of X(883)

X(885)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(7)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(885) lies on these lines:
1,514   7,513   9,522   21,884   104,105   673,900   919,929
X(885) = isotomic conjugate of X(883)

X(886)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(512)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(886) lies on these lines: 99,669   512,670   880,892
X(886) = isogonal conjugate of X(887)
X(886) = isotomic conjugate of X(888)

X(887)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(512)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(887) lies on these lines: 99,670   187,237
X(887) = isogonal conjugate of X(886)

X(888)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(512)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(888) lies on the line at infinity.
X(888) lies on these lines: 30,511   351,865   694,882   805,8925
X(888) = isotomic conjugate of X(886)

X(889)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)], u : v : w = X(513)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(889) lies on these lines: 99,898   190,649   350,903   513,668
X(889) = isogonal conjugate of X(890)
X(889) = isotomic conjugate of X(891)

X(890)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²u(bv - cw)/(a²u² - bcvw), u : v : w = X(513)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(890) lies on these lines: 100,190   187,237
X(890) = isogonal conjugate of X(889)

X(891)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u(bv - cw)/(a²u² - bcvw), u : v : w = X(513)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(891) lies on the line at infinity.
X(891) lies on these lines: 1,659   30,511   244,665   291,876
X(891) = isogonal conjugate of X(898)
X(891) = isotomic conjugate of X(889)

X(892)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a²u² - bcvw)/[a²u(bv - cw)]
                        where u : v : w = X(523)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(892) lies on these lines:
99,523   111,381   290,895   316,524   670,850   805,888   880,886
X(892) = isogonal conjugate of X(351)
X(892) = isotomic conjugate of X(690)

X(893)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/(a² + bc)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(893) lies on these lines:
9,43   19,232   42,694   55,869   100,733   171,292   239,257
X(893) = isogonal conjugate of X(894)

X(894)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (a² + bc)/a
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(894) lies on these lines:
1,87   2,7   6,75   8,193   10,1046   37,86   42,1045   65,257   72,1010   81,314   92,608   141,320   213,274   256,291   273,458   287,651   312,940   319,524   536,1100
X(894) = isogonal conjugate of X(893)
X(894) = isotomic conjugate of X(257)

X(895)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u/(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C),
                        where u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(895) lies on these lines:
4,542   6,110   54,575   65,651   66,193   67,524   69,125   74,511   287,879   290,892
X(895) = isogonal conjugate of X(468)

X(896)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C,
                        where u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(896) lies on these lines:
1,21   9,750   44,513   57,748   162,240   171,756   238,244   518,902
X(896) = isogonal conjugate of X(897)

X(897)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C),
                        where u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(897) lies on these lines:
1,662   10,190   19,162   37,100   65,651   75,799   158,823   225,653   691,759
X(897) = isogonal conjugate of X(896)

X(898)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u/(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C),
                        where u : v : w = X(100)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(898) lies on these lines:
99,889   100,667   101,765   105,666   106,238   813,1023   840,1083
X(898) = isogonal conjugate of X(891)

X(899)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C,
                        where u : v : w = X(100)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(899) lies on these lines:
1,2   6,750   38,210   44,513   55,748   88,291   100,238   244,518

X(900)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C)/u,
                        where u : v : w = X(101)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point that lies on the circumcircle, X(900) lies on the line at infinity.
X(900) lies on these lines:
11,244   30,511   37,665   100,190   335,876   673,885
X(900) = isogonal conjugate of X(901)

X(901)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u/(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C),
                        where u : v : w = X(101)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(901) lies on the circumcircle.
X(901) lies on these lines:
3,953   36,106   55,840   59,109   88,105   100,513   101,649   104,517   484,759   675,903
X(901) = isogonal conjugate of X(900)

X(902)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C)/u,
                        where u : v : w = X(101)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(902) lies on these lines:
1,89   6,31   35,595   36,106   44,678   100,238   109,840   165,614   187,237   518,896   739,813   750,1001
X(902) = isogonal conjugate of X(903)

X(903)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u/[a(v² + w² - 2u² - 2vw cos A + wu cos B + uv cos C)],
                        where u : v : w = X(101)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(903) lies on these lines:
2,45   7,528   27,648   75,537   86,99   310,670   320,519   335,536   350,889   527,666   675,901   812,1022
X(903) = isogonal conjugate of X(902)
X(903) = isotomic conjugate of X(519)

X(904)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²/(a² + bc)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(904) lies on these lines:
1,257   21,238   31,237   55,869   101,733   172,694

X(905)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [wb² - vc² + a(wb - vc)]cos A, u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(905) lies on these lines:
36,238   241,514   441,525   521,656   1053,1054

X(906)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (cos A)/[wb² - vc² + a(wb - vc)], u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(906) lies on these lines:
32,218   41,601   72,248   100,112   101,109   163,692   219,577

X(907)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[wb³ - vc³ + a²(wb - vc)], u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(907) lies on this line: 98,620

X(908)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [(wb + vc)/a - v - w]/a, u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(908) lies on these lines:
1,998   2,7   4,78   5,72   8,946   10,994   11,518   12,960   80,519   92,264   100,516   119,517   153,515   214,535   377,936   392,495   514,661
X(908) = isogonal conjugate of X(909)

X(909)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[(wb + vc)/a - v - w], u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(909) lies on these lines:
9,48   19,604   55,184   163,284   333,662
X(909) = isogonal conjugate of X(908)

X(910)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a[wb² + vc² - a(wb + vc)], u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(910) lies on these lines:
3,169   6,57   9,165   19,25   32,1104   40,220   41,65   44,513   46,218   48,354   101,517   103,971   105,919   118,516   227,607   241,294

X(911)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[wb² + vc² - a(wb + vc)], u : v : w = X(3)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(911) lies on these lines:
3,101   41,603   48,692   56,607   241,294

X(912)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (wb + vc)/a - v - w, u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(912) lies on the line at infinity.
X(912) lies on these lines:
1,90   3,63   5,226   30,511   38,1064   65,68   222,1060   601,976   774,1066   960,993
X(912) = isogonal conjugate of X(915)

X(913)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[(wb + vc)/a - v - w], u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(913) lies on these lines: 19,101   25,692   27,662   571,608
X(913) = isogonal conjugate of X(914)

X(914)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [(wb + vc)/a - v - w]/a, u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(914) lies on these lines: 8,224   63,69   514,661
X(914) = isogonal conjugate of X(913)

X(915)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[(wb + vc)/a - v - w], u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(915) lies on these lines:
3,48   19,101   21,925   24,108   28,110   34,46   99,286   242,929
X(915) = isogonal conjugate of X(912)

X(916)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = wb² + vc² - a(wb + vc), u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(916) lies on the line at infinity.
X(916) lies on these lines:
3,48   30,511   72,185   1037,1069
X(916) = isogonal conjugate of X(917)

X(917)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[wb² + vc² - a(wb + vc)], u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(917) lies on the circumcircle.
X(917) lies on these lines: 4,101   27,110   92,100   109,278
X(917) = isogonal conjugate of X(916)

X(918)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (w/b - v/c)/a², u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point of the circumcircle, X(918) lies on the line at infinity.
X(918) lies on these lines: 30,511   63,654   190,644   1086,1111
X(918) = isogonal conjugate of X(919)
X(918) = isotomic conjugate of X(666)

X(919)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²/(w/b - v/c), u : v : w = X(4)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(919) lies on the circumcircle.
X(919) lies on these lines:
6,840   99,666   100,650   101,663   103,672   104,294   105,910   106,1055   109,649   673,675   885,929
X(919) = isogonal conjugate of X(918)

X(920)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = cos²B cos²C - cos²A
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = f(A,B,C) sin A
X(920) lies on these lines:
1,21   4,46   4,78   9,498   19,91   57,499   158,921   201,601   243,1075
X(921) = isogonal conjugate of X(920)

X(921)
Trilinears        f(A,B,C) : f(B,C,A) : f(C,A,B),
                        where f(A,B,C) = 1/(cos²B cos²C - cos²A)
Barycentrics  g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = f(A,B,C) sin A
X(921) lies on these lines: 19,47   46,225   63,91   158,920
X(921) = isogonal conjugate of X(920)

X(922)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²(cos²B cos²C - 2 cos²A),
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(922) lies on these lines: 31,48   667,788

X(923)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²/(cos²B cos²C - 2 cos²A)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(923) lies on these lines: 1,662   31,163   42,101   213,692   691,741

X(924)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bw - cv, u : v : w = X(5)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(924) lies on the line at infinity.
X(924) lies on these lines: 30,511   50,647   66,879   669,684
X(924) = isogonal conjugate of X(925)

X(925)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(5)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(925) lies on the circumcircle.
X(925) lies on these lines:
2,136   3,847   4,131   20,68   21,915   22,98   91,759   94,96   648,933   842,858
X(925) = isogonal conjugate of X(924)
X(925) = anticomplement of X(136)

X(926)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bw - cv, u : v : w = X(7)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(926) lies on the line at infinity.
X(926) lies on these lines: 30,511   55,654   101,692   295,875   657,663
X(926) = isogonal conjugate of X(927)

X(927)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(7)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(927) lies on the circumcircle.
X(927) lies on these lines:
7,840   100,693   101,514   103,516   109,658   813,1025
X(927) = isogonal conjugate of X(926)

X(928)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bw - cv, u : v : w = X(11)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(928) lies on the line at infinity.
X(928) lies on these lines:
30,511   101,109   102,103   116,124   117,118   151,152   295,876
X(928) = isogonal conjugate of X(929)

X(929)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(11)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(929) lies on the circumcircle.
X(929) lies on these lines: 101,522   102,516   103,515   109,514   242,915   885,919
X(929) = isogonal conjugate of X(928)

X(930)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(17)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(930) lies on the circumcircle.
X(930) lies on these lines:
2,137   3,252   4,128   74,550
X(930) = anticomplement of of X(137)

X(931)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(21)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(931) lies on the circumcircle.
X(931) lies on these lines:
100,645   101,643   108,648   109,662   111,941

X(932)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(43)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(932) lies on the circumcircle.
X(932) lies on these lines:
1,727   21,741   81,715   87,106   105,330   172,699   644,813   667,668

X(933)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(54)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(933) lies on the circumcircle.
X(933) lies on these lines:
4,137   54,74   98,275   250,759   270,759   648,925

X(934)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(56)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(934) lies on the circumcircle.
X(934) lies on these lines:
1,103   3,972   7,104   56,105   77,102   100,658   101,651   106,269   644,1025   675,1088   727,1106   741,1042   759,1014

X(935)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/(bw - cv), u : v : w = X(67)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(935) lies on the circumcircle.
X(935) lies on these lines:
4,842   67,74   98,186   110,525   111,468   112,523   250,827   378,477

X(936)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ - a²(b + c) - a(b - c)² + (b + c)³
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(936) lies on these lines:
1,2   3,9   40,960   56,210   57,72   63,404   165,411   223,1038   226,443   269,307   377,908   581,966   984,988
X(936) = isogonal conjugate of X(937)

X(937)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ - a²(b + c) - a(b - c)² + (b + c)³]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(937) lies on these lines:
1,329   6,40   31,1103   34,196   56,223
X(937) = isogonal conjugate of X(936)

X(938)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[a⁴ - 2a³(b + c) - 4a²bc + (b - c)(b² - c²)(2a - b - c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(938) lies on these lines:
1,2   4,7   20,57   29,81   40,390   56,411   63,452   65,497   354,388   355,1056   517,1058   774,986   944,999
X(938) = isogonal conjugate of X(939)
X(939) = anticomplement of X(936)

X(939)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[a⁴ - 2a³(b + c) - 4a²bc + (b - c)(b² - c²)(2a - b - c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(939) lies on these lines: 3,269   34,55   56,212
X(939) = isogonal conjugate of X(938)

X(940)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a² + a(b + c) + 2bc
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(940) lies on these lines:
1,3   2,6   31,1001   37,63   42,750   58,405   72,975   222,226   312,894   386,474   387,443   518,612
X(940) = isogonal conjugate of X(941)

X(941)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a² + a(b + c) + 2bc]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(941) lies on these lines:
1,573   2,314   6,21   8,37   9,42   81,967   84,581   111,931
X(941) = isogonal conjugate of X(940)

X(942)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 2abc + (b + c)(a - b + c)(a + b - c)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(942) lies on these lines:
1,3   2,72   4,7   5,226   6,169   8,443   10,141   11,113   28,60   30,553   34,222   37,579   42,1066   58,1104   63,405   78,474   212,582   238,1046   277,1002   279,955   284,1100   355,388   496,946   750,976   758,960   962,1058   1042,1064
X(942) = isogonal conjugate of X(943)
X(942) = inverse of X(36) in the incircle
X(942) = complement of X(72)

X(943)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[2abc + (b + c)(a - b + c)(a + b - c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(943) lies on these lines:
1,201   3,7   4,12   8,405   21,72   28,228   35,79   80,950   100,442   500,651   968,1039   1001,1058
X(943) = isogonal conjugate of X(942)

X(944)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[3a⁴ - 2a³(b + c) + (b - c)²(2ab + 2ac - 2bc - b² - c² - 2a²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(944) lies on these lines:
1,4   2,355   3,8   10,631   20,145   30,962   40,376   48,281   80,499   84,1000   150,348   390,971   392,452   938,999   958,1006
X(944) = isogonal conjugate of X(945)
X(944) = anticomplement of X(355)

X(945)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[3a⁴ - 2a³(b + c) + (b - c)²(2ab + 2ac - 2bc - b² - c² - 2a²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(945) lies on these lines: 78,517   283,859
X(945) = isogonal conjugate of X(944)

X(946)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[a³(b + c) + (b - c)²(a² - ab - ac - b² - c² - 2bc)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(946) lies on these lines:
1,4   2,40   3,142   5,10   7,84   8,908   11,65   29,102   30,551   46,499   56,1012   79,104   165,631   238,580   355,381   392,442   496,942   546,952   951,1067
X(946) = isogonal conjugate of X(947)
X(946) = complement of X(40)

X(947)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[a³(b + c) + (b - c)²(a² - ab - ac - b² - c² - 2bc)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(947) lies on these lines:
29,515   40,77   48,282   73,102   219,572   581,1036   950,1067   951,1066
X(947) = isogonal conjugate of X(946)

X(948)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bcvw[a³ - a²(b + c) + a(b + c)² - (b - c)(b² - c²)],
                        where u : v : w = X(9)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(948) lies on these lines:
1,4   2,85   6,7   37,347   57,169   142,269   220,329   307,966   342,393
X(948) = isogonal conjugate of X(949)

X(949)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = au/[a³ - a²(b + c) + a(b + c)² - (b - c)(b² - c²)],
                        where u : v : w = X(9)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(949) lies on these lines:
1,607   2,294   3,41   6,77   48,1037   78,220
X(949) = isogonal conjugate of X(948)

X(950)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc(b + c - a)[2a³ + (b + c)(a² + (b - c)²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(950) lies on these lines:
1,4   8,9   10,55   11,214   20,57   29,284   30,553   35,1006   65,516   72,519   80,943   142,377   145,329   281,380   389,517   440,1104   947,1067
X(950) = isogonal conjugate of X(951)

X(951)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[(b + c - a)[2a³ + (b + c)(a² + (b - c)²)]]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(951) lies on these lines:
29,226   56,219   57,78   73,284   77,738   946,1067   947,1066
X(951) = isogonal conjugate of X(950)

X(952)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[2a⁴ + 2a³(b + c) - a²(b² - 4bc + c²) + (2a - b - c)(b - c)(b² - c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(952) lies on the line at infinity.
X(952) lies on these lines:
1,5   3,8   4,145   10,140   30,511   40,550   150,664   182,996   390,1000   546,946   547,551   572,594
X(952) = isogonal conjugate of X(953)

X(953)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[2a⁴ + 2a³(b + c) - a²(b² - 4bc + c²) + (2a - b - c)(b - c)(b² - c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(953) lies on the circumcircle.
X(953) lies on these lines: 3,901   36,109   100,517   104,513   110,859
X(953) = isogonal conjugate of X(952)

X(954)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a⁵ + (b + c)[2a²(b² + c² - a² + bc) - (b - c)²(2bc + ab + ac)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(954) lies on these lines:
1,6   3,7   4,390   10,480   21,144   55,226   142,474   971,1012   999,1006
X(954) = isogonal conjugate of X(955)

X(955)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a⁵ + (b + c)[2a²(b² + c² - a² + bc) - (b - c)²(2bc + ab + ac)]]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(955) lies on these lines: 57,991   278,354   279,942
X(955) = isogonal conjugate of X(954)

X(956)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ - a(b - c)² - 2bc( b + c)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(956) lies on these lines:
1,6   2,495   3,8   10,56   21,145   55,519   63,517   183,668   210,997   333,859   388,442   452,1058
X(956) = isogonal conjugate of X(957)

X(957)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ - a(b - c)² - 2bc( b + c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(957) lies on these lines: 2,392   57,995   81,859
X(957) = isogonal conjugate of X(956)

X(958)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (b + c - a)(a² + ab + ac + 2bc)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(958) lies on these lines:
1,6   2,12   3,10   8,21   28,281   36,474   40,1012   48,965   64,65   78,210   104,631   198,966   243,318   452,497   944,1006
X(958) = isogonal conjugate of X(959)
X(958) = complement of X(388)

X(959)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[(b + c - a)(a² + ab + ac + 2bc)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(959) lies on these lines:
1,573   2,65   6,961   7,274   8,181   28,608   56,81   57,1042   193,330
X(959) = isogonal conjugate of X(958)

X(960)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = (b + c - a)(b² + c² + ab + ac)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(960) lies on these lines:
1,6   2,65   3,997   5,10   8,210   12,908   19,965   21,60   36,191   40,936   46,474   55,78   56,63   113,123   221,1038   241,1042   329,388   758,942   912,993   978,986
X(960) = isogonal conjugate of X(961)
X(960) = complement of X(65)

X(961)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[(b + c - a)(b² + c² + ab + ac)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(961) lies on these lines:
1,572   2,12   6,959   57,1106   65,81   105,1104   108,429   274,1014
X(961) = isogonal conjugate of X(960)

X(962)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[a⁴ + 2a³(b + c) - 4a²bc - (b + c)(b - c)²(2a + b + c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(962) lies on these lines:
1,7   2,40   4,8   30,944   55,411   65,497   145,515   149,151   278,412   382,952   392,443   484,499   942,1058
X(962) = isogonal conjugate of X(963)
X(962) = anticomplement of X(40)

X(963)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[a⁴ + 2a³(b + c) - 4a²bc - (b + c)(b - c)²(2a + b + c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(963) lies on these lines: 3,200   33,56   48,220   55,603
X(963) = isogonal conjugate of X(962)

X(964)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[a⁴ + (b + c)( a³ + ab² + ac² + abc + (b + c)(a² + bc))]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(964) lies on these lines: 1,321   2,3   6,8   10,31

X(965)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a⁴ - a³(b + c) - a²(b² + c²) + a(b + c)³ + 2bc(b + c)²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(965) lies on these lines:
2,6   3,9   10,219   19,960   37,78   48,958   284,405   474,579

X(966)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = bc[a² - 2a(b + c) - (b + c)²]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(966) lies on these lines:
2,6   4,9   8,37   45,346   198,958   307,948   443,579   572,631   581,936
X(966) = isogonal conjugate of X(967)

X(967)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a/[a² - 2a(b + c) - (b + c)²]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(967) lies on these lines: 3,42   25,58   27,393   37,63   81,941
X(967) = isogonal conjugate of X(966)

X(968)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a² - 2a(b + c) - (b + c)²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(968) lies on these lines:
1,21   9,42   19,25   35,975   45,210   165,750   200,756   614,1001   943,1039
X(968) = isogonal conjugate of X(969)

X(969)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a² - 2a(b + c) - (b + c)²]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(969) lies on these lines: 7,225   10,69   19,81   37,63   65,77   158,286
X(969) = isogonal conjugate of X(968)

X(970)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a[a³(b + c)² + a(ab + ac - 2bc)(b² + c²) - bc(b³ + c³) - a(b⁴ + c⁴) - (b⁵ + c⁵)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(970) lies on these lines: 1,181   3,6   5,10   21,51   40,43   185,411

X(971)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a⁴(b + c) - 2a³(b² + c² - bc) + 2a(b - c)²(b² + c² + bc) - (b - c)²(b + c)³
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
As the isogonal conjugate of a point on the circumcircle, X(971) lies on the line at infinity.
X(971) lies on these lines:
3,9   4,7   5,142   6,990   20,72   30,511   33,222   37,991   103,910   165,210   390,944   954,1012
X(971) = isogonal conjugate of X(972)

X(972)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a⁴(b + c) - 2a³(b² + c² - bc) + 2a(b - c)²(b² + c² + bc) - (b - c)²(b + c)³]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(972) lies on the circumcircle.
X(972) lies on these lines: 3,934   40,101   55,108   100,329   109,165
X(972) = isogonal conjugate of X(971)

X(973) = 1st EHRMANN POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = u[a¹⁰ - 3a⁸s + a⁶(2b⁴ + 3b²c² + 2c⁴)
                                              + a⁴s(2b⁴ - b²c² + 2c⁴) + a²(b² - c²)²(3b⁴ + 5b²c² + 3c⁴)
                                              + s(b² - c²)²(b⁴ - b²c² + c⁴)],
                        where u : v : w = X(51), s = b² + c²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
For constructions of X(973) and X(974), see Hyacinthos message 3695, Sept. 1, 2001, and related messages.
X(973) lies on these lines: 5,15   6,24   68,568

X(974) = 2nd EHRMANN POINT
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = [sa¹⁰ - a⁸(3b⁴ - 2b²c² + 3c⁴) + a⁶s(2b⁴ - 3b²c² + 2c⁴)
                                              + a⁴(b² - c²)²(2b⁴ - 7b²c² + 2c⁴)
                                              - 3a²s(b² - c²)²(b⁴ - 3b²c² + c⁴) + (b² - c²)⁴(b⁴ + b²c² + c⁴)] cos A,
                        where s = b² + c²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
For constructions of X(973) and X(974), see Hyacinthos message 3695, Sept. 1, 2001, and related messages.
X(974) lies on these lines: 5,113   6,74

X(975)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ + a²(b + c) + a(b² + c² + 4bc) + (b + c)³
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(975) lies on these lines:
1,2   3,37   9,58   28,33   35,968   46,750   57,201   72,940   226,1038   312,1010

X(976)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ + (b + c)(b² + c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(976) lies on these lines:
1,2   3,38   21,983   31,72   37,41   66,73   100,986   210,1104   244,474   404,982   405,756   601,912   750,942   1060,1066
X(976) = isogonal conjugate of X(977)

X(977)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ + (b + c)(b² + c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(977) lies on these lines: 22,56   58,982   106,833
X(977) = isogonal conjugate of X(976)

X(978)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²(b + c) + a(b² - bc + c²) - bc(b + c)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(978) lies on these lines:
1,2   3,238   9,39   21,748   31,404   40,1050   46,1054   56,979   57,1046   58,87   72,982   171,474   266,361   631,1064   651,1106   960,986
X(978) = isogonal conjugate of X(979)

X(979)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a²(b + c) + a(b² - bc + c²) - bc(b + c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(979) lies on these lines: 10,87   43,58   56,978
X(979) = isogonal conjugate of X(978)

X(980)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a²(b² + bc + c²) + (b² + c²)(bc + ca + ab)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(980) lies on these lines: 1,3   2,39   32,81   38,869   63,213
X(980) = isogonal conjugate of X(981)

X(981)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a²(b² + bc + c²) + (b² + c²)(bc + ca + ab)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(981) lies on these lines: 6,314   8,213   21,32   256,573
X(981) = isogonal conjugate of X(980)

X(982)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = b² - bc + c²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(982) lies on these lines:
1,3   2,38   7,256   43,518   58,977   63,238   72,978   81,985   222,613   226,262   240,278   257,330   310,871   312,726   404,967   758,995   846,1001
X(982) = isogonal conjugate of X(983)

X(983)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[b² - bc + c²]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(983) lies on these lines: 1,182   7,171   8,238   21,976   55,256
X(983) = isogonal conjugate of X(982)

X(984)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = b² + bc + c²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(984) lies on these lines:
1,6   2,38   8,192   10,75   21,976   43,210   55,846   63,171   100,753   101,761   201,388   240,281   386,872   519,751   936,988
X(984) = isogonal conjugate of X(985)
X(984) = isotomic conjugate of X(870)

X(985)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[b² + bc + c²]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(985) lies on these lines:
1,32   2,31   6,291   58,274   81,982   105,825   279,1106   727,789
X(985) = isogonal conjugate of X(984)

X(986)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a(b² + bc + c²) + b³ + c³
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(986) lies on these lines:
1,3   4,240   6,1046   8,38   10,75   43,72   100,976   194,257   291,337   386,758   405,846   474,1054   774,938   960,978
X(986) = isogonal conjugate of X(987)

X(987)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a(b² + bc + c²) + b³ + c³]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(987) lies on these lines:
3,256   4,171   7,1106   8,31   9,32   58,314
X(987) = isogonal conjugate of X(986)

X(988)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ - a²(b + c) - (3a + b + c)(b² + c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(988) lies on these lines:
1,3   9,39   21,614   38,78   77,1106   84,256   404,612   936,984
X(988) = isogonal conjugate of X(989)

X(989)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ - a²(b + c) - (3a + b + c)(b² + c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(989) lies on these lines: 21,612   40,256   84,171
X(989) = isogonal conjugate of X(988)

X(990)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a⁵ - a⁴(b + c) - 2a³bc - a(b - c)²(b² + c²) + (b - c)²(b + c)³
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(990) lies on these lines:
1,7   3,37   6,971   33,57   58,84   165,612   226,1040

X(991)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a[a³(b + c) - a²(b² - bc + c²) - a(b + c)(b² + c²) + (b - c)(b³ - c³)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(991) lies on these lines:
1,7   3,37   6,971   33,57   58,84   165,612   226,1040

X(992)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³(b + c) + a²(b² + c²) - abc(b + c) - bc(b + c)²
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(992) lies on these lines: 2,6   9,39   44,583   238,1009

X(993)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ - a(b² + c²) - bc(b + c)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(993) lies on these lines:
1,21   2,36   3,10   8,35   9,48   32,1107   55,519   56,226   75,99   87,106   238,995   495,529   516,1012   527,551   912,960
X(993) = isogonal conjugate of X(994)

X(994)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ - a(b² + c²) - bc(b + c)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(994) lies on these lines: 10,908   31,759   37,517   65,386   75,758
X(994) = isogonal conjugate of X(993)

X(995)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a(ab + ac - bc + b² + c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(995) lies on these lines:
1,2   3,595   6,101   31,36   56,58   57,957   238,993   581,1104   609,1055   758,982   991,1064
X(995) = isogonal conjugate of X(996)

X(996)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a(ab + ac - bc + b² + c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(996) lies on these lines: 2,106   6,519   8,58   10,56   182,952
X(996) = isogonal conjugate of X(995)

X(997)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a³ - a²(b + c) - a(b - c)² + (b + c)(b² + c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(997) lies on these lines:
1,2   3,960   9,48   21,90   34,860   36,63   46,404   55,392   56,72   57,758   65,474   141,1060   210,956   518,999
X(997) = isogonal conjugate of X(998)

X(998)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a³ - a²(b + c) - a(b - c)² + (b + c)(b² + c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(998) lies on these lines: 1,908   6,517   46,58   106,614
X(998) = isogonal conjugate of X(997)

X(999)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = a(a² + 4bc - b² - c²)
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(999) lies on these lines: 1,3   2,495   4,496   5,388   6,101   7,104   8,474   11,381   12,499   20,1058   30,497   63,392   77,1057   78,1059   81,859   145,404   329,405   376,390   518,997   527,551   601,1106   938,944   954,1006
X(999) = isogonal conjugate of X(1000)

X(1000)
Trilinears        f(a,b,c) : f(b,c,a) : f(c,a,b),
                        where f(a,b,c) = 1/[a(a² + 4bc - b² - c²)]
Barycentrics  g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(1000) lies on these lines:
1,631   7,517   8,392   9,519   21,145   55,104   79,388   80,497   84,944   390,952
X(1000) = isogonal conjugate of X(999)

Top of Part 5
Part 6
Front Cover