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collinear wanted, rectangles ABCD, AEFG with B,E,D,G collinear given

Source: 2003 Romania JBMO TST3 p1

May 23, 2020

geometryrectanglecollinearcollinearity

Problem Statement

Suppose

ABCD

and

AEFG

are rectangles such that the points

B,E,D,G

are collinear (in this order). Let the lines

BC

and

GF

intersect at point

T

and let the lines

DC

and

EF

intersect at point

H

. Prove that points

A, H

and

T

are collinear.