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Inscribed pentagon

Source: Iran MO 3rd round 2019 finals - Geometry P3

August 14, 2019

geometry

Problem Statement

Given an inscribed pentagon

ABCDE

with circumcircle

\Gamma

. Line

\ell

passes through vertex

A

and is tangent to

\Gamma

. Points

X,Y

lie on

\ell

so that

A

lies between

X

and

Y

. Circumcircle of triangle

XED

intersects segment

AD

at

Q

and circumcircle of triangle

YBC

intersects segment

AC

at

P

. Lines

XE,YB

intersects each other at

S

and lines

XQ, Y P

at

Z

. Prove that circumcircle of triangles

XY Z

and

BES

are tangent.

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