Online Geometry Problem 637: Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos. 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 in ECB is tangent to semicircle D at G. Prove that AE and AG are congruent.