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Geometry

Source: Serbian national olympiad 2022 P1

April 7, 2022

geometrySerbian competition

Problem Statement

Let

k

be incircle of acute triangle

ABC

,

AC\neq BC

, and

l

be excircle that touches

p\cap l = \{Z, T\}

. Line

p

through the

C

is orthogonal to

AB

,

p\cap k = \{X, Y\}

,

p\cap l = \{Z, T\}

and the point arrangement is

X-Y-Z-T

. Circle

m

through

X

and

Z

intersects

AB

at

D

and

E

. Prove that points

D,Y,E,T

are concyclic.

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