Online Geometry Problem 639: Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows the semicircles of diameters AB (center O), and CB (center D). Line CE is perpendicular to AB and the inscribed circle F in ECB is tangent to semicircle D at G. If DF and CE meet at H, prove that DA and DH are congruent.