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inradii 3 times!

Source: Indonesia IMO 2010 TST, Stage 1, Test 3, Problem 4

November 12, 2009
geometryrectangleincenterratiogeometry proposed

Problem Statement

Let ABC ABC be an acute-angled triangle such that there exist points D,E,F D,E,F on side BC,CA,AB BC,CA,AB, respectively such that the inradii of triangle AEF,BDF,CDE AEF,BDF,CDE are all equal to r0 r_0. If the inradii of triangle DEF DEF and ABC ABC are r r and R R, respectively, prove that r\plus{}r_0\equal{}R. Soewono, Bandung
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