D

D

E

E

F

F

39387

39388

X(39387) - Euler line intercept of X(39)X(13758), labeled P
X(39388) - Euler line intercept of X(39)X(13638), labeled Q

Let inner-Vecten circle meet circles with diameters BC, CA, AB
at points A', B', C' not lying on perpendicular bisectors of sides of ABC.
Then lines AA', BB', CC' concur at X(39387).

Let outer-Vecten circle meet circles with diameters BC, CA, AB
at points A'', B'', C'' not lying on perpendicular bisectors of sides of ABC.
Then lines AA'', BB'', CC'' concur at X(39388).

Sketch contributed by Stanisław Majchrzak, June 2021
Drag A, B, C

A = (-7.12, 6.23)
B = (-8.98, 1.4)
C = (-3.65, 1.49)
f = Segment(B, C)
g = Segment(C, A)
h = Segment(A, B)
Mid_a = Midpoint(f)
Mid_b = Midpoint(g)
Mid_c = Midpoint(h)
c = Circle(Mid_a, C)
d = Circle(Mid_b, A)
e = Circle(Mid_c, B)
i = LineBisector(f)
j = LineBisector(g)
k = LineBisector(h)
D_2, D_1 = Intersect(c, i)
E_2, E_1 = Intersect(d, j)
F_2, F_1 = Intersect(e, k)
p = Circle(D_1, E_1, F_1)
q = Circle(D_2, E_2, F_2)
A' = Intersect(c, p, 2)
B' = Intersect(d, p, 2)
C' = Intersect(e, p, 2)
l = Line(A, A')
m = Line(B, B')
n = Line(C, C')
P = Intersect(m, n)
A'' = Intersect(c, q, 2)
B'' = Intersect(d, q, 2)
C'' = Intersect(e, q, 2)
r = Line(A, A'')
s = Line(B, B'')
t = Line(C, C'')
Q = Intersect(s, t)