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A rectangle

Source: Indian RMO 1993 Problem 4

October 23, 2005
geometryrectanglePythagorean Theorem

Problem Statement

Let ABCDABCD be a rectangle with AB=aAB = a and BC=bBC = b. Suppose r1r_1 is the radius of the circle passing through AA and BB touching CDCD; and similarly r2r_2 is the radius of the circle passing through BB and CC and touching ADAD. Show that r1+r2≥58(a+b). r_1 + r_2 \geq \frac{5}{8} ( a + b) .
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