PART 4
X(601)
Trilinears sin2A + cos A : sin2B + cos B : sin2C + cos CBarycentrics (sin A)(sin2A + cos A) : (sin B)(sin2B + cos B) : (sin C)(sin2C + cos C)
X(601) lies on these lines: 1,104 3,31 4,171 5,750 35,47 40,58 41,906 55,255 140,748 165,580 201,920 371,606 372,605 774,1060 912,976 999,1106
X(602)
Trilinears sin2A - cos A : sin2B - cos B : sin2C - cos CBarycentrics (sin A)(sin2A - cos A) : (sin B)(sin2B - cos B) : (sin C)(sin2C - cos C)
X(602) lies on these lines: 1,201 3,31 4,238 5,748 36,47 40,595 56,255 140,750 171,631 371,605 372,606 517,582 774,1062
X(603)
Trilinears cos2A - cos A : cos2B - cos B : cos2C - cos CBarycentrics (sin A)(cos2A - cos A) : (cos B)(cos2B - cos B) : (cos C)(cos2C - cos C)
X(603) lies on these lines: 1,104 3,73 6,1035 12,750 28,34 31,56 33,84 36,47 41,911 48,577 63,201 77,283 171,388 223,580 404,651
X(603) = isogonal conjugate of X(318)
X(604)
Trilinears a(1 - cos A) : b(1 - cos B) : c(1 - cos c)Barycentrics a2(1 - cos A) : b2(1 - cos B) : c2(1 - cos C)
X(604) lies on these lines: 1,572 6,41 19,909 31,184 32,1106 36,573 57,77 65,1100 109,739 219,672 608,1042
X(604) = isogonal conjugate of X(312)
X(605)
Trilinears a(1 + sin A) : b(1 + sin B) : c(1 + sin c)Barycentrics a2(1 + sin A) : b2(1 + sin B) : c2(1 + sin C)
X(605) lies on these lines: 6,31 371,602 372,601 590,748 615,750
X(606)
Trilinears a(1 - sin A) : b(1 - sin B) : c(1 - sin c)Barycentrics a2(1 - sin A) : b2(1 - sin B) : c2(1 - sin C)
X(606) lies on these lines: 6,31 371,601 372,602 590,750 615,748
X(607)
Trilinears a(1 + sec A) : b(1 + sec B) : c(1 + sec c)Barycentrics a2(1 + sec A) : b2(1 + sec B) : c2(1 + sec C)
X(607) lies on these lines: 1,949 4,218 6,19 8,29 9,1039 25,41 28,1002 33,210 56,911 92,239 213,1096 227,910 240,611
X(607) = isogonal conjugate of X(348)
X(608)
Trilinears a(1 - sec A) : b(1 - sec B) : c(1 - sec c)Barycentrics a2(1 - sec A) : b2(1 - sec B) : c2(1 - sec C)
X(608) lies on these lines: 6,19 7,27 9,1041 25,31 28,959 92,894 108,739 109,579 193,651 223,380 240,613 571,913 604,1042
X(608) = isogonal conjugate of X(345)
X(609)
Trilinears area + a2 sin A : area + b2 sin B : area + c2 sin CBarycentrics a(area + a2 sin A) : b(area + b2 sin B) : c(area + c2 sin C)
X(609) lies on these lines: 1,32 6,36 31,101 33,112 41,58 251,614 995,1055
X(610)
Trilinears area - a2 cot A : area - b2 cot B : area - c2 cot CBarycentrics a(area - a2 cot A) : b(area - b2 cot B) : c(area - c2 cot C)
X(610) lies on these lines: 1,19 3,9 6,57 40,219 71,165 159,197 169,572 281,515 326,662
X(611)
Trilinears W + sin A : W + sin B : W + sin C, where W = (a2 + b2 + c2)/(4*area)Barycentrics a(W + sin A) : b(W + sin B) : c(W + sin C)
X(611) lies on these lines: 1,6 55,511 56,182 141,498 240,607 394,612
X(612)
Trilinears W + csc A : W + csc B : W + csc C, where W = (a2 + b2 + c2)/(4*area)Barycentrics a(W + csc A) : b(W + csc B) : c(W + csc C)
X(612) lies on these lines: 1,2 6,210 9,31 12,34 19,25 21,989 22,35 38,57 63,171 165,990 394,611 404,988 495,1060 518,940
X(613)
Trilinears W - sin A : W - sin B : W - sin C, where W = (a2 + b2 + c2)/(4*area)Barycentrics a(W - sin A) : b(W - sin B) : c(W - sin C)
X(613) lies on these lines: 1,6 55,182 56,511 141,499 222,982 240,608 394,614 496,1069
X(614)
Trilinears W - csc A : W - csc B : W - csc C, where W = (a2 + b2 + c2)/(4*area)Barycentrics a(W - csc A) : b(W - csc B) : c(W - csc C)
X(614) lies on these lines: 1,2 6,354 9,38 11,33 21,988 22,36 25,34 31,57 46,595 63,238 106,998 165,902 251,609 269,479 278,1096 305,350 394,613 496,1062 497,1040 968,1001
X(615) = ISOGONAL CONJUGATE OF X(589)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (a2 - 4*area)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a2 - 4*area
X(615) lies on these lines: 2,6 3,486 5,372 32,639 39,641 140,371 591,637 605,750 606,748
X(615) = isogonal conjugate of X(589)
X(615) = complement of X(491)
Centers 616- 642
were contributed by Bernard Gibert, March 2, 2001. Notation:
SA = (b2 + c2 - a2)/2
SB = (c2 + a2 - b2)/2
SC = (a2 + b2 - c2)/2
X(616) = ANTICOMPLEMENT OF X(13)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [SB*SC - 2*SA*(a2 + sqr(3)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
The midpoint of X(616) and X(617) is the Steiner point, X(99).
X(616) lies on these lines: 2,13 3,299 4,627 14,148 15,532 20,633 30,298 69,74 302,381 303,549
X(616) = anticomplement of X(13)
X(617) = ANTICOMPLEMENT OF X(14)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [SB*SC - 2*SA*(a2 - sqr(3)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(617) lies on these lines: 2,14 3,298 4,628 13,148 16,533 20,634 30,299 69,74 302,549 303,381
X(617) = anticomplement of X(14)
X(618) = COMPLEMENT OF X(13)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [2*SB*SC + 5*SA*a2 + 2*sqr(3)*(b2 + c2)*area]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(618) lies on these lines: 2,13 3,635 5,629 14,99 15,298 30,623 39,395 61,627 140,630 141,542 396,532
X(619) = COMPLEMENT OF X(14)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [2*SB*SC + 5*SA*a2 - 2*sqr(3)*(b2 + c2)*area]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(619) lies on these lines:
2,14 3,636 5,630 13,99 16,299 30,624 39,396 62,628 140,629 141,542 395,533
X(620) = MIDPOINT OF X(618) AND X(619)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [4* SA*a2 - (b4 + c4)]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(620) lies on these lines:
2,99 3,114 30,625 98,631 141,542 187,325 230,538
X(620) = complement of X(115)
X(621) = ANTICOMPLEMENT OF X(15)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [sqr(3)*SB*SC + 2*SA*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(621) lies on these lines: 2,14 3,302 4,69 5,303 13,533 20,627 30,298 183,383 265,300 299,381 325,1080 343,472 394,473
X(621) = anticomplement of X(15)
X(622) = ANTICOMPLEMENT OF X(16)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [sqr(3)*SB*SC - 2*SA*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(622) lies on these lines: 2,13 3,303 4,69 5,302 14,532 20,628 30,299 183,1080 265,301 298,381 325,383 343,473 394,472
X(622) = anticomplement of X(16)
X(623) = COMPLEMENT OF X(15)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [2*(b2 + c2)*area + sqr(3)*(SA*a2 + 2*SB*SC)]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(623) lies on these lines: 2,14 3,629 5,141 13,298 16,302 17,633 18,83 30,618 396,533
X(623) = inverse of X(624) in the nine-point circle
X(623) = complement of X(15)
X(624) = COMPLEMENT OF X(16)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [2*(b2 + c2)*area - sqr(3)*(SA*a2 + 2*SB*SC)]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(624) lies on these lines: 2,13 3,630 5,141 14,299 15,303 17,83 30,619 395,532
X(624) = inverse of X(623) in the nine-point circle
X(624) = complement of X(16)
X(625) = MIDPOINT OF X(623) AND X(624)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*(b4 + c4 - b2c2) - a2(b2 + c2)]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(625) lies on these lines: 2,187 5,141 30,620 115,325 126,858 230,754
X(625) = inverse of X(141) in the nine-point circle
X(625) = complement of X(187)
X(626) = COMPLEMENT OF X(32)
Trilinears (b4 + c4)/a : (c4 + a4)/a : (a4 + b4)/aBarycentrics b4 + c4 : c4 + a4 : a4 + b4
X(626) lies on these lines: 2,32 3,114 5,141 10,760 37,746 39,325 76,115 316,384
X(626) = complement of X(32)
X(627) = ANTICOMPLEMENT OF X(17)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [SB*SC + 2*SA*(a2 + sqr(3)*area)]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(627) lies on these lines: 2,17 3,298 4,616 5,302 16,635 20,621 54,69 61,618 140,299
X(627) = anticomplement of X(17)
X(628) = ANTICOMPLEMENT OF X(18)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [SB*SC + 2*SA*(a2 - sqr(3)*area)]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(628) lies on these lines: 2,18 3,299 4,617 5,303 15,636 20,622 54,69 62,619 140,298
X(628) = anticomplement of X(18)
X(629) = COMPLEMENT OF X(17)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [6*SB*SC + 7*SA*a2 + 2*sqr(3)*(b2 + c2)*area]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(629) lies on these lines: 2,17 3,623 5,618 61,302 140,619 141,575
X(629) = complement of X(17)
X(630) = COMPLEMENT OF X(18)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), wheref(a,b,c) = [6*SB*SC + 7*SA*a2 - 2*sqr(3)*(b2 + c2)*area]/a
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(630) lies on these lines: 2,18 3,624 5,619 62,303 140,618 141,575
X(630) = complement of X(18)
X(631) = (3/5)OG
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (SB*SC + 2*SA*a2)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(631) lies on these lines: 1,1000 2,3 10,944 35,497 36,388 54,69 55,1058 56,1056 98,620 104,958 171,602 216,1075 238,601 315,1007 390,496 487,492 488,491 572,966 978,1064
X(632) = (9/10)OG
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (6*SB*SC + 7*SA*a2)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(632) lies on these lines: 2,3 141,575
X(633) = ANTICOMPLEMENT OF X(61)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (SB*SC + 2*sqr(3)*SA*area)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(633) lies on these lines: 2,18 3,298 4,69 5,299 14,636 17,623 20,616 140,302 141,398 343,471 394,470 397,524
X(633) = anticomplement of X(61)
X(634) = ANTICOMPLEMENT OF X(62)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (SB*SC - 2*sqr(3)*SA*area)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(634) lies on these lines: 2,17 3,299 4,69 5,298 13,635 18,624 20,617 140,303 141,397 343,470 394,471 398,524
X(634) = anticomplement of X(62)
X(635) = COMPLEMENT OF X(61)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + SA*a2 + 2*sqr(3)*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(635) lies on these lines: 2,18 3,618 5,141 13,634 16,627 17,299 62,298 140,619 397,532
X(635) = complement of X(61)
X(636) = COMPLEMENT OF X(62)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + SA*a2 - 2*sqr(3)*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(636) lies on these lines: 2,17 3,619 5,141 14,633 15,628 18,298 61,299 140,618 398,533
X(636) = complement of X(62)
X(637) = ANTICOMPLEMENT OF X(371)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (SB*SC + 2*SA*area)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(637) lies on these lines: 2,371 3,489 4,69 5,491 20,488 30,490 591,615
X(637) = anticomplement of X(371)
X(638) = ANTICOMPLEMENT OF X(372)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (SB*SC - 2*SA*area)/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(638) lies on these lines: 2,372 3,490 4,69 5,492 20,487 30,489
X(638) = anticomplement of X(372)
X(639) = COMPLEMENT OF X(371)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + SA*a2 + 2*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(639) lies on these lines: 2,371 3,641 5,141 32,615 69,485 315,372
X(639) = complement of X(371)
X(640) = COMPLEMENT OF X(372)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + SA*a2 - 2*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(640) lies on these lines: 2,372 3,642 5,141 69,486 315,371
X(640) = complement of X(372)
X(641) = COMPLEMENT OF X(485)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + 3*SA*a2 + 2*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(641) lies on these lines: 2,372 3,639 39,615 140,141 371,492
X(641) = complement of X(485)
X(642) = COMPLEMENT OF X(486)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [2*SB*SC + 3*SA*a2 - 2*(b2 + c2)*area]/aBarycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(642) lies on these lines: 2,371 3,640 140,141 372,491
X(642) = complement of X(486)
X(643) = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)/(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(643) satisfies the equation X*(incircle) = Kiepert parabola, where * denotes trilinear multiplication, defined by
(u : v : w) * (x : y : z) = ux : vy : wz.
X(643) lies on these lines: 8,1098 99,109 100,110 101,931 162,190 163,1018 212,312 283,1043
X(644) = TRILINEAR MULTIPLIER FOR YFF PARABOLA
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (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(644) satisfies the equation X*(incircle) = Yff parabola, where * denotes trilinear multiplication, defined by
(u : v : w) * (x : y : z) = ux : vy : wz.
X(644) lies on these lines: 8,220 78,728 100,101 105,1083 145,218 190,651 219,346 645,646 666,668 813,932 934,1025
X(645) = BARYCENTRIC MULTIPLIER FOR KIEPERT PARABOLA
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)/[a(b2 - c2)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b + c - a)/(b2 - c2)
X(645) satisfies the equation X*(incircle) = Kiepert parabola, where * denotes barycentric multiplication, defined by
(u : v : w) * (x : y : z) = ux : vy : wz (barycentric coordinates; see note at X(2)).
X(645) lies on these lines: 9,261 99,101 100,931 294,314 644,646 648,668 651,799 666,670
X(646) = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)/[a2(b - c)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b + c - a)/[a(b - c)]
X(646) satisfies the equation X*(incircle) = Yff parabola, where * denotes barycentric multiplication, defined by
(u : v : w) * (x : y : z) = ux : vy : wz (barycentric coordinates, see note at X(2)).
X(646) lies on these lines: 190,668,646 644,646
X(647) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF EULER LINE
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b2 - c2)(b2 + c2 - a2)= u(A,B,C) : u(B,C,A) : u(C,A,B), where u(A,B,C) = sin 2A sin(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(647) is the point whose trilinears are coefficients for the Euler line.
X(647) lies on these lines: 1,1021 2,850 50,654 111,842 184,878 187,237 230,231 441,525 520,652
X(647) = isogonal conjugate of X(648)
X(647) = complement of X(850)
X(648) = TRILINEAR POLE OF EULER LINE
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a(b2 - c2)(b2 + c2 - a2)]= u(A,B,C) : u(B,C,A) : u(C,A,B), where u(A,B,C) = csc 2A csc(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(648) is constructed as the pole of the Euler line L as follows: let A", B", C" be the points where L meets the sidelines BC, CA, AB of the reference triangle ABC. Let A', B', C' be the harmonic conjugates of A", B", C" with respect to {B,C}, {C,A}, {A,B}, respectively, The lines AA', BB', CC' concur in X(648).
X(648) lies on these lines:
4,452 6,264 27,903 94,275 95,216 99,112 107,110 108,931 132,147 155,1093 162,190 185,1105 193,317 232,385 249,687 250,523 297,340 447,519 645,668 651,823 653,662 925,933 1020,1021 1075,1092
X(648) = isogonal conjugate of X(647)
X(648) = isotomic conjugate of X(525)
X(649) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(2)
Trilinears a(b - c) : b(c - a) : c(a - b)Barycentrics a2(b - c) : b2(c - a) : c2(a - b)
X(649) lies on these lines:
31,884 42,788 44,513 57,1024 89,1022 100,660 101,901 109,919 187,237 190,889 239,514 693,812
X(649) = isogonal conjugate of X(650)
X(650) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(3)
Trilinears cos B - cos C : cos C - cos A : cos A - cos B= (b - c)(b + c - a) : (c - a)(c + a - b) : (a - b)(a + b - c)
Barycentrics sin A (cos B - cos C) : sin B (cos C - cos A) : sin C(cos A - cos B)
= a(b - c)(b + c - a) : b(c - a)(c + a - b) : c(a - b)(a + b - c)
X(650) lies on these lines:
2,693 44,513 55,884 100,919 230,231 241,514 521,1021 663,861
X(650) = isogonal conjugate of X(651)
X(650) = complement of X(693)
X(651) = TRILINEAR POLE OF LINE X(1)X(3)
Trilinears 1/(cos B - cos C) : 1/(cos C - cos A) : 1/(cos A - cos B)= 1/[(b - c)(b + c - a)] : 1/[(c - a)(c + a - b)] : 1[(a - b)(a + b - c)]
Barycentrics (sin A)/(cos B - cos C) : (sin B)/(cos C - cos A) : (sin C)/(cos A - cos B)
= a/[(b - c)(b + c - a)] : b/[(c - a)(c + a - b)] : c/[(a - b)(a + b - c)]
X(651) lies on these lines:
2,222 6,7 8,221 9,77 21,73 44,241 57,88 59,513 63,223 65,895 69,478 81,226 100,109 101,934 108,110 144,219 155,1068 190,644 193,608 218,279 255,411 287,894 329,394 404,603 500,943 514,655 645,799 648,823 978,1106
X(651) = isogonal conjugate of X(650)
X(652) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(4)
Trilinears sec B - sec C : sec C - sec A : sec A - sec BBarycentrics sin A (sec B - sec C) : sin B (sec C - sec A) : sin C(sec A - sec B)
X(652) lies on these lines: 44,513 243,522 520,647
X(652) = isogonal conjugate of X(653)
X(653) = TRILINEAR POLE OF LINE X(1)X(4)
Trilinears 1/(sec B - sec C) : 1/(sec C - sec A) : 1/(sec A - sec B)Barycentrics (sin A)/(sec B - sec C) : (sin B)/(sec C - sec A) : (sin C)/(sec A - sec B)
X(653) lies on these lines:
2,196 7,281 9,342 19,273 29,65 46,158 57,92 78,207 88,278 100,108 107,109 208,318 225,897 648,662
X(653) = isogonal conjugate of X(652)
X(654) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(5)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos(A - B) - cos(C - 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(654) lies on these lines: 44,513 50,647 55,926 63,918 101,109
X(654) = isogonal conjugate of X(655)
X(655) = TRILINEAR POLE OF LINE X(1)X(5)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[cos(A - B) - cos(C - 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(655) lies on these lines: 59,523 80,516 100,522 514,651
X(655) = isogonal conjugate of X(654)
X(656) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(19)
Trilinears tan B - tan C : tan C - tan A : tan A - tan BBarycentrics sin A (tan B - tan C) : sin B (tan C - tan A) : sin C (tan A - tan B)
X(656) lies on these lines: 44,513 240,522 521,810 662,1101 667,832
X(656) = isogonal conjugate of X(162)
X(656) = isotomic conjugate of X(811)
X(657) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(30)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (1 + cos A)(cos B - cos 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(657) lies on these lines: 9,522 44,513 59,101 663,853
X(657) = isogonal conjugate of X(658)
X(658) = TRILINEAR POLE OF LINE X(1)X(30)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[(1 + cos A)(cos B - cos 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(658) lies on these lines:
7,11 57,673 88,279 100,664 109,927 190,1020
X(658) = isogonal conjugate of X(657)
X(659) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(39)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (a2 - 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(659) lies on these lines:
1,891 23,385 44,513 100,190 105,884 291,875 292,665 514,667
X(659) = isogonal conjugate of X(660)
X(660) = TRILINEAR POLE OF LINE X(1)X(39)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[(a2 - 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(660) lies on these lines:
44,292 88,291 100,649 190,513 239,335 320,334 512,1016 662,765
X(660) = isogonal conjugate of X(659)
X(661) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(1)X(63)
Trilinears cot B - cot C : cot C - cot A : cot A - cot BBarycentrics sin A (cot B - cot C) : sin B (cot C - cot A) : sin C (cot A - cot B)
X(661) lies on these lines: 44,513 514,693 663,810
X(661) = isogonal conjugate of X(662)
X(661) = isotomic conjugate of X(799)
X(662) = TRILINEAR POLE OF LINE X(1)X(63)
Trilinears 1/(cot B - cot C) : 1/(cot C - cot A) : 1/(cot A - cot B)Barycentrics (sin A)/(cot B - cot C) : (sin B)/(cot C - cot A) : (sin C)/(cot A - cot B)
X(662) lies on these lines:
1,897 3,1098 6,757 27,913 48,75 60,404 81,88 86,142 99,101 100,110 109,931 214,759 243,425 261,572 326,610 333,909 648,653 656,1101 660,765 689,787 775,820 811,823 827,831
X(662) = isogonal conjugate of X(661)
X(663) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(7)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b - c)(b + c - a)Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(663) lies on these lines:
1,514 41,884 101,919 106,840 187,237 513,855 650,861 657,853 661,810
X(663) = isogonal conjugate of X(664)
X(664) = TRILINEAR POLE OF LINE X(2)X(7)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a(b - c)(b + c - a)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(664) lies on these lines:
1,85 7,528 8,348 69,347 73,290 75,77 99,109 100,658 101,514 145,279 150,952 175,490 176,489 190,644 223,312 226,671 239,241 307,319 322,326 648,653 668,1026 1018,1025
X(664) = isogonal conjugate of X(663)
X(664) = isotomic conjugate of X(522)
X(665) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(11)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a[(a - b)2(a + b - c) - (c - a)2(c + a - b)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(665) lies on these lines:
37,900 101,109 187,237 241,514 244,866 292,659 743,761
X(665) = isogonal conjugate of X(666)
X(666) = TRILINEAR POLE OF LINE X(2)X(11)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/[a - b)2(a + b - c) - (c - a)2(c + a - b)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(666) lies on these lines:
99,919 101,514 105,898 190,522 239,294 527,673 644,668 645,670 1026,1027
X(666) = isogonal conjugate of X(665)
X(666) = isotomic conjugate of X(918)
X(667) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(37)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a2(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(667) lies on these lines:
3,1083 36,238 56,764 100,898 101,813 187,237 213,875 514,659 656,832 668,932 692,1110 788,798
X(667) = isogonal conjugate of X(668)
X(667) = inverse of X(1083) in the circumcircle
X(668) = TRILINEAR POLE OF LINE X(2)X(37)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a2(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(668) lies on these lines:
2,1015 8,76 10,274 69,150 72,290 75,537 80,313 99,100 101,789 110,839 190,646 304,341 321,671 350,519 513,889 644,666 645,648 664,1026 667,932
X(668) = isogonal conjugate of X(667)
X(668) = isotomic conjugate of X(513)
X(668) = anticomplement of X(1015)
X(669) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(39)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a3(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(669) lies on these lines:
23,385 25,878 31,875 99,886 110,805 187,237 684,924 688,864 804,850
X(669) = isogonal conjugate of X(670)
X(670) = TRILINEAR POLE OF LINE X(2)X(39)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a3(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(670) lies on these lines: 2,1084 69,290 76,338 99,804 110,689 141,308 190,799 310,903 512,886 645,666 850,892
X(670) = isogonal conjugate of X(669)
X(670) = isotomic conjugate of X(512)
X(670) = anticomplement of X(1084)
X(671) = TRILINEAR POLE OF LINE X(2)X(99)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a(2a2 - 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(671) lies on these lines:
2,99 4,542 6,598 10,190 13,531 14,530 30,98 76,338 83,597 226,664 262,381 316,524 321,668 485,489 486,490
X(671) = isogonal conjugate of X(187)
X(671) = isotomic conjugate of X(524)
X(672) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(100)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a[b2 + c2 - 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(672) lies on these lines:
1,1002 2,7 3,41 6,31 36,101 37,38 39,213 43,165 44,513 46,169 56,220 72,1009 103,919 105,238 190,350 219,604 519,1018
X(672) = isogonal conjugate of X(673)
X(673) = TRILINEAR POLE OF LINE X(2)X(100)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/[b2 + c2 - 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(673) lies on these lines:
2,11 6,7 9,75 19,273 27,162 57,658 86,142 238,516 239,335 310,333 527,666 675,919 812,1024 885,900
X(673) = isogonal conjugate of X(672)
X(674) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(2)X(101)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a[b3 + c3 - a(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(674) lies on the line at infinity.
X(674) lies on these lines: 6,31 30,511 51,210
X(674) = isogonal conjugate of X(675)
X(675) = TRILINEAR POLE OF LINE X(2)X(101)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/[b3 + c3 - a(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(675) lies on the circumcircle.
X(675) lies on these lines:
2,101 7,109 27,112 75,100 86,110 99,310 108,273 335,813 673,919 789,871 901,903 934,1088
X(675) = isogonal conjugate of X(674)
X(676) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(3)X(101)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(b - c)[b3 + c3 - a3 + (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(676) lies on this line: 514,551
X(676) = isogonal conjugate of X(677)
X(677) = TRILINEAR POLE OF LINE X(3)X(101)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/{(b - c)[b3 + c3 - a3 + (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(677) = isogonal conjugate of X(676)
X(678)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - 2a)2Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(678) lies on these lines: 1,88 44,902 45,55
X(678) = isogonal conjugate of X(679)
X(679)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/(b + c - 2a)2Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(679) lies on these lines: 44,88 320,519
X(679) = isogonal conjugate of X(678)
X(680) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(4)X(9)
Trilinears sin B sec2C - sin C sec2B : sin C sec2A - sin A sec2C : sin A sec2B - sin B sec2ABarycentrics csc C sec2C - csc B sec2B : csc A sec2A - csc C sec2C : csc B sec2B - csc A sec2A
As the isogonal conjugate of a point on the circumcircle, X(680) lies on the line at infinity.
X(680) lies on this line: 30,511
X(680) = isogonal conjugate of X(681)
X(681) = TRILINEAR POLE OF LINE X(4)X(9)
Trilinears f(A,B,C): f(B,C,A) : f(C,A,B), where f(A,B,C) = cos2A (sin B cos2B - sin C 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(681) lies on the circumcircle.
X(681) lies on this line: 110,823
X(681) = isogonal conjugate of X(680)
X(682) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(4)X(76)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec B csc3C + sec C csc3BBarycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
X(682) lies on these lines: 3,69 154,237 248,695
X(682) = isogonal conjugate of X(683)
X(683) = TRILINEAR POLE OF LINE X(4)X(76)
Trilinears f(A,B,C): f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[sec B csc3C + sec C csc3B]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(683) lies on this line: 25,305
X(683) = isogonal conjugate of X(682)
X(684) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(4)X(98)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec B sin3 C - sec C sin3 BBarycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin A f(A,B,C)
X(684) lies on these lines: 110,351 114,132 122,125 147,804 325,523 520,647 669,924
X(684) = isogonal conjugate of X(685)
X(685) = TRILINEAR POLE OF LINE X(4)X(98)
Trilinears f(A,B,C): f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(sec B sin3 C - sec C sin3 B)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(685) lies on these lines: 98,468 110,850 250,523 287,297
X(685) = isogonal conjugate of X(684)
X(686) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(4)X(110)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec B csc(A - B) + sec C 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(686) lies on these lines: 115,125 184,351 520,647
X(686) = isogonal conjugate of X(687)
X(687) = TRILINEAR POLE OF LINE X(4)X(110)
Trilinears f(A,B,C): f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[sec B csc(A - B) + sec C 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(687) lies on these lines: 107,250 249,648
X(687) = isogonal conjugate of X(686)
X(688) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(6)X(99)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a3(b4 - c4)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(688) lies on the line at infinity.
X(688) lies on this line: 6,882 30,511 669,864 798,872
X(688) = isogonal conjugate of X(689)
X(689) = TRILINEAR POLE OF LINE X(6)X(99)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a3(b4 - c4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(689) lies on the circumcircle.
X(689) lies on these lines:
1,719 2,733 6,703 75,745 76,755 82,715 83,729 110,670 111,308 251,699 662,787 741,873 799,813
X(689) = isogonal conjugate of X(688)
X(690) = ISOGONAL CONJUGATE OF TRILINEAR POLE OF LINE X(6)X(110)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(b2 - c2)(2a2 - 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(690) lies on the line at infinity.
X(690) lies on these lines:
30,511 74,98 99,110 113,114 115,125 146,147
X(690) = isogonal conjugate of X(691)
X(690) = isotomic conjugate of X(892)
X(691) = TRILINEAR POLE OF LINE X(6)X(110)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[(b2 - c2)(2a2 - 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(691) lies on the circumcircle.
X(691) lies on these lines:
3,842 6,843 23,111 30,98 74,511 99,523 110,249 112,250 316,858 376,477 741,923 759,897 805,882
X(691) = isogonal conjugate of X(690)
X(692)
Trilinears a2/(b - c) : b2/(c - a) c2/(a - b)Barycentrics a3/(b - c) : b3/(c - a) c3/(a - b)
X(692) lies on these lines:
25,913 48,911 55,184 59,513 99,785 100,110 101,926 154,197 163,906 182,1001 206,219 213,923 667,1110 813,825
X(692) = isogonal conjugate of X(693)
X(693)
Trilinears (b - c)/a2 : (c - a)/b2 : (a - b)/c2Barycentrics (b - c)/a : (c - a)/b : (a - b)/c
X(693) lies on these lines:
2,650 76,764 100,927 320,350 321,824 325,523 514,661 649,812
X(693) = isogonal conjugate of X(692)
X(693) = isotomic conjugate of X(100)
X(693) = anticomplement of X(650)
X(694) = ISOGONAL CONJUGATE OF X(385)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(a4 - b2c2)Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(694) lies on these lines:
6,1084 37,256 42,893 110,251 111,805 141,308 172,904 257,335 351,881 384,695 882,888
X(694) = isogonal conjugate of X(385)
X(695) = ISOGONAL CONJUGATE OF X(384)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/(a4 + b2c2)Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(695) lies on these lines: 69,194 99,711 248,682 384,694
X(695) = isogonal conjugate of X(384)
X(696) = EVEN (- 4, - 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b-3 + c-3) - a-4(b-4 + c-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(696) lies on the line at infinity. The first trilinear coordinate has the form
am-1(bn + cn) - an-1(bm + cm).
If m and n are distinct integers, this form fits the definition of even polynomial center as in Clark Kimberling, "Functional equations associated with triangle geometry," Aequationes Mathematicae 45 (1993) 127-152. This form, perhaps appearing initially here (July 7, 2001) defines a triangle center for arbitrary distinct real numbers m and n. Selected even infinity and circumcircle points begin at X(696); odd ones begin at X(768).
Certain points of this type occur prior to this section. They are as follows:
X(538) = even (- 2, 0) infinity point
X(536) = even (- 1, 0) infinity point
X(519) = even (0, 1) infinity point
X(106) = even (0, 1) circumcircle point
X(524) = even (0, 2) infinity point
X(111) = even (0, 2) circumcircle point
X(518) = even (1, 2) infinity point
X(105) = even (1, 2) circumcircle point
X(674) = even (2, 3) infinity point
X(675) = even (2, 3) circumcircle point
X(511) = even (2, 4) infinity point
X(98) = even (2, 4) circumcircle point
X(696) lies on these lines: 30,511 313,561
X(696) = isogonal conjugate of X(697)
X(697) = EVEN (- 4, - 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b-3 + c-3) - a-4(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(697) lies on the circumcircle. This is one of several points of the form given by first trilinear
1/[am-1(bn + cn) - an-1(bm + cm)],
hence the name "(m, n)-circumcircle point".
X(697) lies on this line: 100,560
X(697) = isogonal conjugate of X(696)
X(698) = EVEN (- 4, - 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b-2 + c-2) - a-3(b-4 + c-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(698) lies on the line at infinity.
X(698) lies on these lines: 6,194 30,511 75,257 76,141
X(698) = isogonal conjugate of X(699)
X(699) = EVEN (- 4, - 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b-2 + c-2) - a-3(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(699) lies on the circumcircle.
X(699) lies on these lines: 32,99 172,932 251,689
X(699) = isogonal conjugate of X(698)
X(700) = EVEN (- 4, - 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b-1 + c-1) - a-2(b-4 + c-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(700) lies on the line at infinity.
X(700) lies on this line: 30,511 75,871
X(700) = isogonal conjugate of X(701)
X(701) = EVEN (- 4, - 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b-1 + c-1) - a-2(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(701) lies on the circumcircle.
X(701) lies on this line: 31,789
X(701) = isogonal conjugate of X(700)
X(702) = EVEN (- 4, 0) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b0 + c0) - a-1(b-4 + c-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(702) lies on the line at infinity.
X(702) lies on these lines: 2,308 30,511
X(702) = isogonal conjugate of X(703)
X(703) = EVEN (- 4, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b0 + c0) - a-1(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(703) lies on the circumcircle.
X(703) lies on this line: 6,689
X(703) = isogonal conjugate of X(702)
X(704) = EVEN (- 4, 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b1 + c1) - a0(b-4 + c-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(704) lies on the line at infinity.
X(704) lies on this line: 30,511
X(704) = isogonal conjugate of X(705)
X(705) = EVEN (- 4, 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b1 + c1) - a0(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(705) lies on the circumcircle.
X(705) = isogonal conjugate of X(704)
X(706) = EVEN (- 4, 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b2 + c2) - a1(b-4 + c-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(706) lies on the line at infinity.
X(706) lies on this line: 30,511
X(706) = isogonal conjugate of X(707)
X(707) = EVEN (- 4, 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b2 + c2) - a1(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(707) lies on the circumcircle.
X(707) = isogonal conjugate of X(706)
X(708) = EVEN (- 4, 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b3 + c3) - a2(b-4 + c-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(708) lies on the line at infinity.
X(708) lies on this line: 30,511
X(708) = isogonal conjugate of X(709)
X(709) = EVEN (- 4, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b3 + c3) - a2(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(709) lies on the circumcircle.
X(709) = isogonal conjugate of X(708)
X(710) = EVEN (- 4, 4) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b4 + c4) - a3(b-4 + c-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(710) lies on the line at infinity.
X(710) lies on this line: 30,511
X(710) = isogonal conjugate of X(711)
X(711) = EVEN (- 4, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b4 + c4) - a3(b-4 + c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(711) lies on the circumcircle.
X(711) lies on this line: 99,695
X(711) = isogonal conjugate of X(710)
X(712) = EVEN (- 3, - 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b-2 + c-2) - a-3(b-3 + 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(712) lies on the line at infinity.
X(712) lies on these lines: 30,511 76,321
X(712) = isogonal conjugate of X(713)
X(713) = EVEN (- 3, - 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b-2 + c-2) - a-3(b-3 + 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(713) lies on the circumcircle.
X(713) lies on these lines: 32,100 101,560
X(713) = isogonal conjugate of X(712)
X(714) = EVEN (- 3, - 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b-1 + c-1) - a-2(b-3 + 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(714) lies on the line at infinity.
X(714) lies on these lines: 30,511 38,75
X(714) = isogonal conjugate of X(715)
X(715) = EVEN (- 3, - 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b-1 + c-1) - a-2(b-3 + 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(715) lies on the circumcircle.
X(715) lies on these lines: 31,99 81,932 82,689 110,560
X(715) = isogonal conjugate of X(714)
X(716) = EVEN (- 3, 0) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b0 + c0) - a-1(b-3 + 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(716) lies on the line at infinity.
X(716) lies on these lines: 2,561 30,511
X(716) = isogonal conjugate of X(717)
X(717) = EVEN (- 3, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b0 + c0) - a-1(b-3 + 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(717) lies on the circumcircle.
X(717) lies on thse lines: 6,789 560,825
X(717) = isogonal conjugate of X(716)
X(718) = EVEN (- 3, 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b1 + c1) - a0(b-3 + 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(718) lies on the line at infinity.
X(718) lies on these lines: 1,561 30,511
X(718) = isogonal conjugate of X(717)
X(719) = EVEN (- 3, 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b1 + c1) - a0(b-3 + 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(719) lies on the circumcircle.
X(719) lies on this line: 1,689 560,827
X(719) = isogonal conjugate of X(718)
X(720) = EVEN (- 3, 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b2 + c2) - a1(b-3 + 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(720) lies on the line at infinity.
X(720) lies on these lines: 6,561 30,511
X(720) = isogonal conjugate of X(721)
X(721) = EVEN (- 3, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b2 + c2) - a1(b-3 + 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(721) lies on the circumcircle.
X(721) = isogonal conjugate of X(720)
X(722) = EVEN (- 3, 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b3 + c3) - a2(b-3 + 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(722) lies on the line at infinity.
X(722) lies on this line: 30,511
X(722) = isogonal conjugate of X(723)
X(723) = EVEN (- 3, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b3 + c3) - a2(b-3 + 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(723) lies on the circumcircle.
X(723) = isogonal conjugate of X(722)
X(724) = EVEN (- 3, 4) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b4 + c4) - a3(b-3 + 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(724) lies on the line at infinity.
X(724) lies on this line: 30,511
X(724) = isogonal conjugate of X(725)
X(725) = EVEN (- 3, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b4 + c4) - a3(b-3 + 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(725) lies on the circumcircle.
X(725) = isogonal conjugate of X(724)
X(726) = EVEN (- 2, -1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-3(b-1 + c-1) - a-2(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(726) lies on the line at infinity.
X(726) lies on these lines: 1,87 10,75 30,511 37,39 38,321 190,238 291,350 312,982
X(726) = isogonal conjugate of X(727)
X(727) = EVEN (- 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(b-1 + c-1) - a-2(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(727) lies on the circumcircle.
X(727) lies on these lines: 1,932 31,43 32,101 58,99 789,985 934,1106
X(727) = isogonal conjugate of X(728)
X(728)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)3Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(728) lies on these lines: 8,9 40,1018 57,345 78,644 200,220
X(728) = isogonal conjugate of X(738)
X(729) = EVEN (- 2, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-3(b0 + c0) - a-1(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(729) lies on the circumcircle.
X(729) lies on these lines: 6,99 32,110 83,689 100,213 187,805
X(729) = isogonal conjugate of X(538)
X(730) = EVEN (- 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(730) lies on the line at infinity.
X(730) lies on these lines: 1,76 8,194 10,39 30,511
X(730) = isogonal conjugate of X(727)
X(731) = EVEN (- 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(731) lies on the circumcircle.
X(731) lies on these lines: 1,789 32,825 100,869
X(731) = isogonal conjugate of X(730)
X(732) = EVEN (- 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(732) lies on the line at infinity.
X(732) lies on these lines: 6,76 30,511 39,141 69,194
X(732) = isogonal conjugate of X(733)
X(733) = EVEN (- 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(733) lies on the circumcircle.
X(733) lies on these lines: 2,689 32,827 39,83 39,141 100,893 101,904 110,251 755,882
X(733) = isogonal conjugate of X(732)
X(734) = EVEN (- 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(733) lies on the line at infinity.
X(734) lies on these lines: 30,511 31,76
X(734) = isogonal conjugate of X(735)
X(735) = EVEN (- 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(735) lies on the circumcircle.
X(735) = isogonal conjugate of X(734)
X(736) = EVEN (- 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(736) lies on the line at infinity.
X(736) lies on these lines: 30,511 32,76 39,325 194,315
X(736) = isogonal conjugate of X(737)
X(737) = EVEN (- 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(737) lies on the circumcircle.
X(737) = isogonal conjugate of X(736)
X(738)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)-3Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(738) lies on these lines: 9,348 56,269 57,279 77,951
X(738) = isogonal conjugate of X(728)
X(739) = EVEN (- 1, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-2(b0 + c0) - a-1(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(739) lies on the circumcircle.
X(739) lies on these lines:
6,100 31,101 81,99 108,608 109,604 813,902
X(739) = isogonal conjugate of X(737)
X(740) = EVEN (- 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(740) lies on the line at infinity.
X(740) lies on these lines:
1,75 8,192 10,37 30,511 42,321 43,312 238,239 872,1089
X(740) = isogonal conjugate of X(741)
X(741) = EVEN (- 1, 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(741) lies on the circumcircle.
X(741) lies on these lines: 1,99 21,932 31,110 42,81 58,101 86,789 107,1096 334,839 335,835 689,873 691,923 759,876 827,849 934,1042
X(741) = isogonal conjugate of X(740)
X(742) = EVEN (- 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(742) lies on the line at infinity.
X(742) lies on these lines: 6,75 30,511 37,141 69,192 320,335
X(742) = isogonal conjugate of X(743)
X(743) = EVEN (- 1, 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(743) lies on the circumcircle.
X(743) lies on these lines: 2,789 31,825 101,869 665,761
X(743) = isogonal conjugate of X(742)
X(744) = EVEN (- 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(744) lies on the line at infinity.
X(744) lies on these lines: 30,511 31,75
X(744) = isogonal conjugate of X(745)
X(745) = EVEN (- 1, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(745) lies on the circumcircle.
X(745) lies on these lines: 31,827 38,99 75,689
X(745) = isogonal conjugate of X(744)
X(746) = EVEN (- 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(746) lies on the line at infinity.
X(746) lies on these lines: 30,511 32,75 37,626 192,315
X(746) = isogonal conjugate of X(747)
X(747) = EVEN (- 1, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(747) lies on the circumcircle.
X(747) = isogonal conjugate of X(746)
X(748)
Trilinears a2 - 2bc : b2 - 2ca : c2 - 2abBarycentrics a3 - 2abc : b3 - 2abc : c3 - 2abc
X(748) lies on these lines: 1,756 2,31 5,602 9,38 11,212 21,978 42,1001 44,354 55,899 63,244 140,601 181,373 255,499 590,605 606,615
X(748) = isogonal conjugate of X(749)
X(749)
Trilinears 1/(a2 - 2bc) : 1/(b2 - 2ca) : 1/(c2 - 2ab)Barycentrics a/(a2 - 2bc) : b/(b2 - 2ca) : c/(c2 - 2ab)
X(749) = isogonal conjugate of X(748)
X(750)
Trilinears a2 + 2bc : b2 + 2ca : c2 + 2abBarycentrics a3 + 2abc : b3 + 2abc : c3 + 2abc
X(750) lies on these lines:
1,88 2,31 5,601 6,899 9,896 12,603 38,57 42,940 43,81 46,975 63,756 140,602 165,968 255,498 388,1106 590,606 605,615 902,1001 942,976
X(750) = isogonal conjugate of X(751)
X(751)
Trilinears 1/(a2 + 2bc) : 1/(b2 + 2ca) : 1/(c2 + 2ab)Barycentrics a/(a2 + 2bc) : b/(b2 + 2ca) : c/(c2 + 2ab)
X(751) = isogonal conjugate of X(750)
X(751) lies on this line: 519,984
X(752) = EVEN (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(752) lies on the line at infinity.
X(752) lies on these lines: 1,320 2,31 10,44 30,511
X(752) = isogonal conjugate of X(753)
X(753) = EVEN (0, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(753) lies on the circumcircle.
X(753) lies on these lines: 6,825 75,789 100,984
X(753) = isogonal conjugate of X(752)
X(754) = EVEN (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(754) lies on the line at infinity.
X(754) lies on these lines: 2,32 30,511 115,316 187,325 230,625
X(754) = isogonal conjugate of X(755)
X(755) = EVEN (0, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(755) lies on the circumcircle.
X(755) lies on these lines: 6,827 39,110 76,689 99,141 733,882
X(755) = isogonal conjugate of X(754)
X(756)
Trilinears (b + c)2 : (c + a)2 : (a + b)2Barycentrics a(b + c)2 : b(c + a)2 : c(a + b)2
X(756) lies on these lines: 1,748 2,38 9,31 10,321 12,201 37,42 45,55 63,750 100,846 171,896 200,968 405,976
X(756) = isogonal conjugate of X(757)
X(756) = isotomic conjugate of X(873)
X(757)
Trilinears (b + c)-2 : (c + a)-2 : (a + b)-2Barycentrics a(b + c)-2 : b(c + a)-2 : c(a + b)-2
X(757) lies on these lines: 6,662 58,86 60,1014 81,593 171,319 763,849
X(757) = isogonal conjugate of X(756)
X(757) = isotomic conjugate of X(1089)
X(758) = EVEN (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(758) lies on the line at infinity.
X(758) lies on these lines: 1,21 8,79 10,12 30,511 36,214 46,78 57,997 100,484 354,392 386,986 942,960 982,995
X(758) = isogonal conjugate of X(757)
X(759) = EVEN (1, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(759) lies on the circumcircle.
X(759) lies on these lines:
1,60 10,21 19,112 28,108 31,994 37,101 58,65 75,99 82,827 91,925 107,158 214,662 270,933 484,901 691,897 741,876 833,1010 840,1019 934,1014
X(759) = isogonal conjugate of X(754)
X(760) = EVEN (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(761) lies on the line at infinity.
X(760) lies on these lines: 1,32 8,315 10,626 30,511
X(760) = isogonal conjugate of X(761)
X(761) = EVEN (1, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(761) lies on the circumcircle.
X(761) lies on this line: 1,825 76,789 101,984 665,743
X(761) = isogonal conjugate of X(762)
X(762)
Trilinears (b + c)3 : (c + a)3 : (a + b)3Barycentrics a(b + c)3 : b(c + a)3 : c(a + b)3
X(762) lies on this line: 210,213 594,1089
X(762) = isogonal conjugate of X(763)
X(763)
Trilinears (b + c)-3 : (c + a)-3 : (a + b)-3Barycentrics a(b + c)-3 : b(c + a)-3 : c(a + b)-3
X(763) lies on line 757,849
X(763) = isogonal conjugate of X(762)
X(764)
Trilinears (b - c)3 : (c - a)3 : (a - b)3Barycentrics a(b - c)3 : b(c - a)3 : c(a - b)3
X(764) lies on these lines: 1,513 10,514 56,667 76,693
X(765)
Trilinears (b - c)-2 : (c - a)-2 : (a - b)-2Barycentrics a(b - c)-2 : b(c - a)-2 : c(a - b)-2
X(765) lies on these lines: 1,1052 59,518 100,513 101,898 109,522 238,519 660,662 798,813
X(765) = isogonal conjugate of X(244)
X(765) = isotomic conjugate of X(1111)
X(766) = EVEN (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(766) lies on the line at infinity.
X(766) lies on these lines: 30,511 31,32
X(766) = isogonal conjugate of X(767)
X(767) = EVEN (3, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a/[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(767) lies on the circumcircle.
X(767) lies on these lines: 75,101 76,100 85,109 108,331 110,274 112,286 334,813 825,870
X(767) = isogonal conjugate of X(766)
X(768) = ODD (- 4, - 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b-3 - c-3) + a-4(b-4 - c-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(768) lies on the line at infinity. The first trilinear coordinate has the form
am-1(bn - cn) + an-1(bm - cm),
corresponding to an odd polynomial center in case m and n are distinct integers. See the note accompanying X(696), where even (m,n) infinity points and even (m,n) circumcircle points are introduced. [For nonzero n, "odd (m,n) circumcircle point" is would be a misnomer (as the point is an even polynomial center); consequently, the prefix o- is used to distinguish this point from "even (m,n) circumcircle point" defined at X(696).] Certain points of these classes occur prior to this section. They are as follows:
X(523) = odd (- 4, - 2) infinity point
X(688) = odd (- 4, 0) infinity point
X(689) = o-(- 4, 0) circumcircle point
X(514) = odd (- 2, - 1) infinity point
X(101) = o-(- 2, - 1) circumcircle point
X(512) = odd (- 2, 0) infinity point
X(99) = o-(- 2, 0) circumcircle point
X(513) = odd (- 1, 0) infinity point
X(100) = o-(- 1, 0) circumcircle point
X(514) = odd (0, 1) infinity point
X(101) = o-(0, 1) circumcircle point
X(523) = odd (0, 2) infinity point
X(110) = o-(0, 2) circumcircle point
X(513) = odd (1, 2) infinity point
X(100) = o-(1, 2) circumcircle point
X(512) = odd (2, 4) infinity point
X(99) = o-(2, 4) circumcircle point
X(768) lies on this line: 30,511
X(768) = isogonal conjugate of X(769)
X(769) = o-(- 4, - 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b-3 - c-3) + a-4(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(769) lies on the circumcircle. This is one of several points of the form given by first trilinear
1/[am-1(bn - cn) + an-1(bm - cm)],
hence the name "(m, n)-circumcircle point".
X(769) = isogonal conjugate of X(768)
X(770)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos3B - cos3CBarycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(770) lies on this line: 44,513
X(770) = isogonal conjugate of X(771)
X(771)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(cos3B - cos3C)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(771) = isogonal conjugate of X(770)
X(772) = ODD (- 4, - 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b-1 - c-1) + a-2(b-4 - c-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(772) lies on the line at infinity.
X(772) lies on this line: 30,511
X(772) = isogonal conjugate of X(773)
X(773) = o-(- 4, - 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b-1 - c-1) + a-2(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(773) lies on the circumcircle.
X(773) = isogonal conjugate of X(772)
X(774)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos2B + cos2CBarycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
X(774) lies on these lines: 1,21 55,201 601,1060 602,1062 821,823 912,1066 938,986
X(774) = isogonal conjugate of X(775)
X(775)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[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(775) lies on these lines: 10,801 31,1097 158,255 225,412 662,820
X(775) = isogonal conjugate of X(774)
X(776) = ODD (- 4, 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b1 - c1) + a0(b-4 - c-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(776) lies on the line at infinity.
X(776) lies on this line: 30,511
X(776) = isogonal conjugate of X(773)
X(777) = o-(- 4, 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b1 - c1) + a0(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(777) lies on the circumcircle.
X(777) = isogonal conjugate of X(776)
X(778) = ODD (- 4, 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b2 - c2) + a1(b-4 - c-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(778) lies on the line at infinity.
X(778) lies on this line: 30,511
X(778) = isogonal conjugate of X(779)
X(779) = o-(- 4, 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b2 - c2) + a1(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(779) lies on the circumcircle.
X(779) = isogonal conjugate of X(778)
X(780) = ODD (- 4, 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b3 - c3) + a2(b-4 - c-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(780) lies on the line at infinity.
X(780) lies on this line: 30,511
X(780) = isogonal conjugate of X(781)
X(781) = o-(- 4, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b3 - c3) + a2(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(781) lies on the circumcircle.
X(781) = isogonal conjugate of X(780)
X(782) = ODD (- 4, 4) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-5(b4 - c4) + a3(b-4 - c-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(782) lies on the line at infinity.
X(782) lies on this line: 30,511
X(782) = isogonal conjugate of X(783)
X(783) = o-(- 4, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-5(b4 - c4) + a3(b-4 - c-4)]Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(783) lies on the circumcircle.
X(783) = isogonal conjugate of X(782)
X(784) = ODD (- 3, - 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b-2 - c-2) + a-3(b-3 - 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(784) lies on the line at infinity.
X(784) lies on this line: 30,511
X(784) = isogonal conjugate of X(785)
X(785) = o-(- 3, - 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b-2 - c-2) + a-3(b-3 - 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(785) lies on the circumcircle.
X(785) lies on this line: 99,692
X(785) = isogonal conjugate of X(782)
X(786) = ODD (- 3, - 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b-1 - c-1) + a-2(b-3 - 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(786) lies on the line at infinity.
X(786) lies on this line: 30,511
X(786) = isogonal conjugate of X(787)
X(787) = o-(- 3, - 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b-1 - c-1) + a-2(b-3 - 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(787) lies on the circumcircle.
X(787) lies on this line: 662,689
X(787) = isogonal conjugate of X(786)
X(788) = ODD (- 3, 0) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b0 - c0) + a-1(b-3 - c-3) =(b3 - c3)/aBarycentrics 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(788) lies on the line at infinity.
X(788) lies on these lines: 30,511 42,649 667,798
X(788) = isogonal conjugate of X(789)
X(789) = o-(- 3, 0) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b0 - c0) + a-1(b-3 - c-3)]=a/(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(789) lies on the circumcircle.
X(789) lies on these lines:
1,731 2,743 6,717 31,701 75,753 76,761 86,741 100,874 101,668 106,870 110,799 112,811 190,813 675,871 727,985
X(789) = isogonal conjugate of X(788)
X(790) = ODD (- 3, 1) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b1 - c1) + a0(b-3 - 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(790) lies on the line at infinity.
X(790) lies on this line: 30,511
X(790) = isogonal conjugate of X(791)
X(791) = o-(- 3, 1) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b1 - c1) + a0(b-3 - 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(791) lies on the circumcircle.
X(791) = isogonal conjugate of X(790)
X(792) = ODD (- 3, 2) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b2 - c2) + a1(b-3 - 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(792) lies on the line at infinity.
X(792) lies on this line: 30,511
X(792) = isogonal conjugate of X(793)
X(793) = o-(- 3, 2) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b2 - c2) + a1(b-3 - 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(793) lies on the circumcircle.
X(793) = isogonal conjugate of X(792)
X(794) = ODD (- 3, 3) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b3 - c3) + a2(b-3 - 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(794) lies on the line at infinity.
X(794) lies on this line: 30,511
X(794) = isogonal conjugate of X(795)
X(795) = o-(- 3, 3) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b3 - c3) + a2(b-3 - 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(795) lies on the circumcircle.
X(795) = isogonal conjugate of X(794)
X(796) = ODD (- 3, 4) INFINITY POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a-4(b4 - c4) + a3(b-3 - 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(794) lies on the line at infinity.
X(796) lies on this line: 30,511
X(796) = isogonal conjugate of X(797)
X(797) = o-(- 3, 4) CIRCUMCIRCLE POINT
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = 1/[a-4(b4 - c4) + a3(b-3 - 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(797) lies on the circumcircle.
X(797) = isogonal conjugate of X(796)
X(798)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin2A (cos2B - cos2C)Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin3A (cos2B - cos2C)
X(798) lies on these lines: 44,513 163,1101 667,788 688,872 765,813
X(798) = isogonal conjugate of X(799)
X(799)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = csc2A/(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(799) lies on these lines:
2,873 63,561 75,897 88,274 99,100 110,789 162,811 190,670 310,333 645,651 689,813
X(799) = isogonal conjugate of X(798)
X(800)
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sin A (cos2B + cos2C)Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sin2A (cos2B + cos2C)
X(800) lies on these lines: 3,6 53,115 232,459 393,1093
X(800) = isogonal conjugate of X(801)