Problem 506. Triangle with Three Squares, Center, Midpoint, Perpendicular, Congruence. Level: High School, College, SAT Prep.
The drawing shows a triangle ABC with the squares
ABDE, BCGH and ACPQ. M is the midpoint of EG and O is the center
of the square ACPQ. Prove that: (1) AMCO is another square, (2)
MD and MH are congruent and perpendicular.