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Geometry 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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Triangle, Incircle, Inradius

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius.

 

Triangle, Circle, Tangent

Proposed Problem 452.
Triangle, Circle, Tangent, Proportional Segments.

 

Triangle, median

Proposed Problem 451.
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Triangle, Median, Cevian

Proposed Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments.

 

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