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Medial line of a triangle

Source: Sharygin 2019 Finals Day 2 Grade 9 P3

July 31, 2019

Problem Statement

Let the incircle

\omega

of

\triangle ABC

touch

AC

and

AB

at points

E

and

F

respectively. Points

X

,

Y

of

\omega

are such that

\angle BXC=\angle BYC=90^{\circ}

. Prove that

EF

and

XY

meet on the medial line of

ABC

.

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