MathDB

Last Problem :D

Source: 2019 Taiwan TST Round 3

April 2, 2020

geometrycircumcircleincentergeometric transformationreflection

Problem Statement

Given a triangle

\triangle{ABC}

with circumcircle

\Omega

. Denote its incenter and

A

-excenter by

I, J

, respectively. Let

T

be the reflection of

J

w.r.t

BC

and

P

is the intersection of

BC

and

AT

. If the circumcircle of

\triangle{AIP}

intersects

BC

at

X \neq P

and there is a point

Y \neq A

on

\Omega

such that

IA = IY

. Show that

\odot\left(IXY\right)

tangents to the line

AI

.

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