Problem 364. Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area. Level: High School, College, SAT Prep.

The figure shows an obtuse triangle ABC (angle B obtuse) of area S. D is the circumcenter of triangle ABC. Circles of diameters AD, BD, and CD form a curvilinear triangle of area S₁. Prove that S = 2S₁.