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2 equal circles inscribed in an angle, common tangent

Source: II Soros Olympiad 1995-96 R3 9.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 4, 2024
geometryequal circles

Problem Statement

Two disjoint circles are inscribed in an angle with vertex AA, whose measure is equal to aa. The distance between their centers is dd. A straight line tangent to both circles and not passing through AA intersects the sides of the angle at points BB and CC. Find the radius of the circle circumscribed about triangle ABCABC.
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