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.