MathDB

5

Part of 1993 Poland - Second Round

Problems(1)

3 triangles with same inradii given, r_1 +r_2 =r wanted

Source: Polish second round 1993 p5

1/19/2020
Let D,E,FD,E,F be points on the sides BC,CA,ABBC,CA,AB of a triangle ABCABC, respectively. Suppose that the inradii of the triangles AEF,BFD,CDEAEF,BFD,CDE are all equal to r1r_1. If r2r_2 and rr are the inradii of triangles DEFDEF and ABCABC respectively, prove that r1+r2=rr_1 +r_2 =r.
geometryinradiusSumincircle