Problem 293: Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity. Level: High School, College, SAT Prep.

The figure shows a quadrilateral ABCD inscribed in a circle. AE and CF are perpendicular to BD, and BG and DH are perpendicular to AC. AEFM and DHGN are rectangles. MFQ and PGN are isosceles right triangles. Prove that triangles BGP and CFQ have equal area.