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A, P, Q are collinear

Source: Junior Olympiad of Malaysia Shortlist 2015 G3

July 17, 2015

geometry

Problem Statement

Let

ABC

a triangle. Let

D

on

AB

and

E

on

AC

such that

DE||BC

. Let line

DE

intersect circumcircle of

ABC

at two distinct points

F

and

G

so that line segments

BF

and

CG

intersect at P. Let circumcircle of

GDP

and

FEP

intersect again at

Q

. Prove that

A, P, Q

are collinear.

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