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2 circles tangent to an arc and a line

Source: III Soros Olympiad 1996-97 R3 11.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 31, 2024
geometrytangent circles

Problem Statement

A chord ABAB is drawn in a certain circle. The smaller of the two arcs ABAB corresponds to a central angle of 120o120^o. A tangent pp to this arc is drawn. Two circles with radii RR and rr are constructed, touching this smaller arc ABAB and straight lines ABAB and pp. Find the radius of the original circle.
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