MathDB

Let

ABC

be a triangle and let

D

and

E

be points on sides

AB

and

AC

, respectively, such that

DE \parallel BC

. Let

P

be any point interior to triangle

ADE

, and let

F

and

G

be the intersections of

DE

with the lines

BP

and

CP

, respectively. Let

Q

be the second intersection point of the circumcircles of triangles

PDG

and

PFE

. Prove that the points

A,P,

and

Q

are collinear.

Problem Statement