MathDB
Czech republic,district round,2009,problem 2

Source:

February 18, 2012
inequalitiestrigonometrygeometry proposedgeometry

Problem Statement

in a right-angled triangle ABCABC with ∠C=90\angle C=90,a,b,ca,b,c are the corresponding sides.Circles K.LK.L have their centers on a,ba,b and are tangent to b,cb,c;a,ca,c respectively,with radii r,tr,t.find the greatest real number pp such that the inequality 1r+1t≥p(1a+1b)\frac{1}{r}+\frac{1}{t}\ge p(\frac{1}{a}+\frac{1}{b}) always holds.
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