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a+b+c>r+r_a+r_b+r_c

Source: India tst 2003 p8

March 15, 2012
geometryinradiusgeometry proposed

Problem Statement

Let ABCABC be a triangle, and let r,r1,r2,r3r, r_1, r_2, r_3 denoted its inradius and the exradii opposite the vertices A,B,CA,B,C, respectively. Suppose a>r1,b>r2,c>r3a>r_1, b>r_2, c>r_3. Prove that (a) triangle ABCABC is acute, (b) a+b+c>r+r1+r2+r3a+b+c>r+r_1+r_2+r_3.
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