MathDB

The equilateral triangle

ABC

is inscribed in the circle

w

. Points

F

and

E

on the sides

AB

and

AC

, respectively, are chosen such that

\angle ABE+ \angle ACF = 60^o

. The circumscribed circle of

\vartriangle AFE

intersects the circle

w

at the point

D

for the second time. The rays

DE

and

DF

intersect the line

BC

at the points

X

and

Y

, respectively. Prove that the center of the inscribed circle of

\vartriangle DXY

does not depend on the choice of points

F

and

E

.
(Hilko Danilo)

Problem Statement