Online Geometry
Problem 673: Internally tangent circles, Chord, Tangent,
Metric Relations. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows the circles O and O'
tangent internally at A with a chord BC tangent to circle O'
at D. Chords AB and AC intersect the circle O' at points E and F,
respectively. If BC = a, AE = e, AF = f, and CD = x, prove that: .