MathDB

A convex hexagon

ABCDEF

with an interior point

P

is given. Assume that

BCEF

is a square and both

ABP

and

PCD

are right isosceles triangles with right angles at

B

and

C

, respectively. Lines

AF

and

DE

intersect at

G

. Prove that

GP

is perpendicular to

BC

.
Proposed by Patrik Bak - Slovakia

Problem Statement