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Again a circle with center A from Balkans

Source: Kosovo MO 2022 Grade 12 Problem 3

March 5, 2022

geometryKosovosimsonparallelism

Problem Statement

Let

\bigtriangleup ABC

be a triangle and

D

be a point in line

BC

such that

AD

bisects

\angle BAC

. Furthermore, let

F

and

G

be points on the circumcircle of

\bigtriangleup ABC

and

E\neq D

point in line

BC

such that

AF=AE=AD=AG

. If

X

and

Y

are the feet of perpendiculars from

D

to

EF

and

EG,

respectively. Prove that

XY\parallel AD

.

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