Geometry problem (2)

Given triangle ABC, angle BAC < 90 degrees. Two squares with side AB, AC are drawn outside of the triangle. M is a midpoint of BC. Show that DM ⊥ ME and DM = ME

Geometry Problems (1): Prove that points are laying on one circle!

Given arbitrary five-wings star, the circumscribed circles of its wings are drawn. Show that intersections points A, B, C, D, E are laying on one circle!