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Classic incenter configurations again

Source: KoMaL A. 840

January 11, 2023

geometryincenterkomal

Problem Statement

The incircle of triangle

ABC

touches the sides in

X

,

Y

and

Z

. In triangle

XYZ

the feet of the altitude from

X

and

Y

are

X'

and

Y'

, respectively. Let line

X'Y'

intersect the circumcircle of triangle

ABC

at

P

and

Q

. Prove that points

X

,

Y

,

P

and

Q

are concyclic.
Proposed by László Simon, Budapest

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