MathDB

Let

{ABC}

be a triangle. Line l is parallel to

{BC}

and it respectively intersects side

{AB}

at point

{D}

, side

{AC}

at point

{E}

, and the circumcircle of the triangle

{ABC}

at points

{F}

and

{G}

, where points

{F,D,E,G}

lie in this order on l. The circumcircles of triangles

{FEB}

and

{DGC}

intersect at points

{P}

and

{Q}

. Prove that points

{A, P,Q}

are collinear.
(Slovakia)

Problem Statement