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Problem 453: Intersecting Circles, Tangent, Circular Segment, Congruence, Area

The figure shows the intersecting circles O and O' at A and B. Line CO is tangent to circle O' at O, lines CDA and CO' are chords of circle O. Prove that the circular segments S and S' are congruent.
A circular segment is an area of a circle enclosed between a chord and the arc whose endpoints equal the chord's.

Intersecting circles





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