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intersection of circumcircles lies on a line

Source: Bosnia and Herzegovina EGMO TST 2019 p3

August 1, 2019

geometrycircumcircle

Problem Statement

The circle inscribed in the triangle

ABC

touches the sides

AB

and

AC

at the points

K

and

L

, respectively. The angle bisectors from

B

and

C

intersect the altitude of the triangle from the vertex

A

at the points

Q

and

R

, respectively. Prove that one of the points of intersection of the circles circumscribed around the triangles

BKQ

and

CPL

lies on

BC