

Online Geometry
Problem 635: Semicircle, Diameter, Perpendicular,
Inscribed Circle, Radius. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows the semicircles of diameters AB (center O,
radius R), and CB (center D, radius r). Line CE
is perpendicular to AB and x is
the radius of the inscribed circle in ECB. Prove
that
.







