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Isosceles Trapezoid

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November 17, 2005
geometrytrapezoidanalytic geometryquadraticsUSAMTSalgebra

Problem Statement

Let ABCDABCD be an isosceles trapezoid, whose dimensions are AB=6AB = 6, BC=5=DABC=5=DA, and CD=4CD=4. Draw circles of radius 3 centered at AA and BB, and circles of radius 2 centered at CC and DD. A circle contained within the trapezoid is tangent to all four of these circles. Its radius is −k+mnp\frac{-k+m\sqrt{n}}p, where kk, mm, nn, and pp are positive integers, nn is not divisible by the square of any prime, and kk and pp are relatively prime. Find k+m+n+pk+m+n+p.
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