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The center of (IPQ) is on BC

Source: Oral Moscow geometry olympiad 2023 8-9.4

April 20, 2023

geometry

Problem Statement

Let

I

be the incenter of triangle

ABC

, tangent to sides

AB

and

AC

at points

E

and

F

, respectively. The lines through

E

and

F

parallel to

AI

intersect lines

BI

and

CI

at points

P

and

Q

, respectively. Prove that the center of the circumcircle of triangle

IPQ

lies on line

BC