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circumcircles of 3 triangles are equal, so are the incircles

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1996 p6

February 20, 2020
incirclecircumcirclegeometry

Problem Statement

Let K,L,MK,L,M be points on sides AB,BC,CAAB,BC,CA, respectively, of a triangle ABCABC such that AK/AB=BL/BC=CM/CA=1/3AK/AB = BL/BC = CM/CA = 1/3. Show that if the circumcircles of the triangles AKM,BLK,CMLAKM, BLK, CML are equal, then so are the incircles of these triangles.
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