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Three concurrent chords in a circle

Source: Kosovo TST 2024 P2

March 19, 2024

TSTgeometrycircleChordsconcurrent linesTangents

Problem Statement

Let

\omega

be a circle and let

A

be a point lying outside of

\omega

. The tangents from

A

to

\omega

touch

\omega

at points

B

and

C

. Let

M

be the midpoint of

BC

and let

D

a point on the side

BC

different from

M

. The circle with diameter

AD

intersects

\omega

at points

X

and

Y

and the circumcircle of

\bigtriangleup ABC

again at

E

. Prove that

AD

,

EM

, and

XY

are concurrent.

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