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China Mathematical Olympiad 1989 problem4

Source: China Mathematical Olympiad 1989 problem4

October 28, 2013
geometryChina

Problem Statement

Given a triangle ABCABC, points D,E,FD,E,F lie on sides BC,CA,ABBC,CA,AB respectively. Moreover, the radii of incircles of △AEF,△BFD,△CDE\triangle AEF, \triangle BFD, \triangle CDE are equal to rr. Denote by r0r_0 and RR the radii of incircles of △DEF\triangle DEF and △ABC\triangle ABC respectively. Prove that r+r0=Rr+r_0=R.
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