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6 points on a circle

Source: Turkey National Mathematical Olympiad 2021 P3

January 6, 2022

geometry

Problem Statement

A circle

\Gamma

is tangent to the side

BC

of a triangle

ABC

at

X

and tangent to the side

AC

at

Y

. A point

P

is taken on the side

AB

. Let

XP

and

YP

intersect

\Gamma

at

K

and

L

for the second time,

AK

and

BL

intersect

\Gamma

at

R

and

S

for the second time. Prove that

XR

and

YS

intersect on

AB

.

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