Problem 503. Triangle with Three Squares, Perpendicular, Congruence, Concurrency. Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with the squares of centers M, N, and O constructed on the sides AB, BC, and AC, respectively. Prove that (1) BO and MN are congruent and perpendicular, (2) AN, BO, and CM are concurrent at P.