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Circles through A, tangent to DE

Source: Macedonian TST 2022, P4

May 21, 2022

geometry

Problem Statement

Given is an acute triangle

Y

with

AB<AC

with altitudes

BD

and

CE

. Let the tangents to the circumcircle at

B

and

C

meet at

Y

. Let

\omega_1

be the circle through

A

tangent to

DE

at

E

; define

\omega_2

similarly, and let their intersection point be

X

. Prove that

A, X, Y

are colinear.

<span class='latex-italic'>Proposed by Nikola Velov</span>

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