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Angle bisectors meets the circumcircle

Source: 2016 Azerbaijan JBMO TST, D2 P2

July 29, 2023

geometryangle bisectorcircumcircle

Problem Statement

Let the angle bisectors of

\angle BAC,

AB

and

\angle ACB

meets the circumcircle of

\triangle ABC

at the points

M,N,

and

K,

respectively. Let the segments

AB

and

MK

intersects at the point

P

and the segments

AC

and

MN

intersects at the point

Q.

Prove that

PQ\parallel BC

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