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EX=EY wanted, 3 circles related

Source: 2021 Dutch IMO TST 2.1

December 29, 2021

equal segmentsgeometry

Problem Statement

Let

\Gamma

be the circumscribed circle of a triangle

ABC

and let

D

be a point at line segment

BC

. The circle passing through

B

and

D

tangent to

\Gamma

and the circle passing through

C

and

D

tangent to

\Gamma

intersect at a point

E \ne D

. The line

DE

intersects

\Gamma

at two points

X

and

Y

. Prove that

|EX| = |EY|

.

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