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Property of circumcenter of triangle determined by reflections

Source: KoMaL A. 844

February 11, 2023

geometrycircumcirclegeometric transformationreflectionkomal

Problem Statement

The inscribed circle of triangle

ABC

is tangent to sides

BC

,

AC

and

AB

at points

D

,

E

and

F

, respectively. Let

E'

be the reflection of point

E

across line

DF

, and

F'

be the reflection of point

F

across line

DE

. Let line

EF

intersect the circumcircle of triangle

AE'F'

at points

X

and

Y

. Prove that

DX=DY

.
Proposed by Márton Lovas, Budapest

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