MathDB

Congenial concyclicity

Source: Kyiv City MO 2024 Round 1, Problem 8.3

January 28, 2024

geometryConcyclic

Problem Statement

The circle

\gamma

passing through the vertex

A

of triangle

ABC

intersects its sides

AB

and

AC

for the second time at points

X

and

Y

, respectively. Also, the circle

\gamma

intersects side

BC

at points

D

and

E

so that

AD = AE

. Prove that the points

B, X, Y, C

lie on the same circle.
Proposed by Mykhailo Shtandenko