MathDB

29

Part of 1971 IMO Longlists

Problems(1)

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

Source:

1/1/2011
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.
geometryrhombusgeometry proposed