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Sign of a+b-2r-2r

Source: Chinese Mathematical Olympiad 2000 Problem 1

August 18, 2013
geometrycircumcircleinradiusgeometry unsolved

Problem Statement

The sides a,b,ca,b,c of triangle ABCABC satisfy a≤b≤ca\le b\le c. The circumradius and inradius of triangle ABCABC are RR and rr respectively. Let f=a+b−2R−2rf=a+b-2R-2r. Determine the sign of ff by the measure of angle CC.
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