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: .