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Radii of circles tangent to incircle of rhombus [ILL 1971]

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January 1, 2011
geometryrhombusgeometry proposed

Problem Statement

A rhombus with its incircle is given. At each vertex of the rhombus a circle is constructed that touches the incircle and two edges of the rhombus. These circles have radii r1,r2r_1,r_2, while the incircle has radius rr. Given that r1r_1 and r2r_2 are natural numbers and that r1r2=rr_1r_2=r, find r1,r2,r_1,r_2, and rr.
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