MathDB

An I for an I

Source: 2020 ISL G8

July 20, 2021

geometryincentercircumcircleIMO ShortlistIMO Shortlist 2020tangentcollinear

Problem Statement

Let

ABC

be a triangle with incenter

I

and circumcircle

\Gamma

. Circles

\omega_{B}

passing through

B

and

\omega_{C}

passing through

C

are tangent at

I

. Let

\omega_{B}

meet minor arc

AB

of

\Gamma

at

P

and

AB

at

M\neq B

, and let

\omega_{C}

meet minor arc

AC

of

\Gamma

at

Q

and

AC

at

N\neq C

. Rays

PM

and

QN

meet at

X

. Let

Y

be a point such that

YB

is tangent to

\omega_{B}

and

YC

is tangent to

\omega_{C}

.
Show that

A,X,Y

are collinear.

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