Online Geometry Problem 636: Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent. 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 the common tangent GM passes through A.