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Spoiler alert: √(ac/2) inversion!

Source: Sharygin Finals 2022 9.3

July 31, 2022

geometry

Problem Statement

A medial line parallel to the side

AC

of triangle

ABC

meets its circumcircle at points at

X

and

Y

. Let

I

be the incenter of triangle

ABC

and

D

be the midpoint of arc

AC

not containing

B

.A point

L

lie on segment

DI

in such a way that

DL= BI/2

. Prove that

\angle IXL = \angle IYL

.

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