Problem

Source: 2018 Taiwan TST Round 1, Test 2, Problem 3

Tags: geometry, coaxial circles, coaxal circles, incenter, Inversion



Given six points $ A, B, C, D, E, F $ such that $ \triangle BCD \stackrel{+}{\sim} \triangle ECA \stackrel{+}{\sim} \triangle BFA $ and let $ I $ be the incenter of $ \triangle ABC. $ Prove that the circumcenter of $ \triangle AID, \triangle BIE, \triangle CIF $ are collinear. Proposed by Telv Cohl