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Return of Geometry Prodigy

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 10.3

April 5, 2023

geometrytangency

Problem Statement

Let

I

be the incenter of the triangle

ABC

, and

P

be any point on the arc

BAC

of its circumcircle. Points

K

and

L

are chosen on the tangent to the circumcircle

\omega

of triangle

API

at point

I

, so that

BK = KI

and

CL = LI

. Show that the circumcircle of triangle

PKL

is tangent to

\omega

.
Proposed by Mykhailo Shtandenko