GeoBunny Sangaku problem 3 (GEOM-10)

A sketch to investigate a sangaku-style problem from GeoBunnies. In a right triangle formed in a semicircle, inscribe a rectangle. In each smaller triangle, formed by the rectangle, inscribe a circle. Find the arrangement so that the area of the two smaller circles equals the larger. Or, the sum of the smaller radii squared is equal to the larger radius squared. Original:
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