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Concyclic points

Source: IMAR 2017, Problem 1

November 18, 2017
geometry

Problem Statement

Let PP be a point in the interior △ABC\triangle ABC, and AD,BE,CFAD,BE,CF 3 concurrent cevians through PP, with D,E,FD,E,F on BC,CA,ABBC,CA,AB. The circle with the diameter BCBC intersects the circle with the diameter ADAD in D1,D2D_1,D_2. Analogously we define E1,E2E_1,E_2 and F1,F2F_1,F_2. Prove that D1,D2,E1,E2,F1,F2D_1,D_2,E_1,E_2,F_1,F_2 are concylic.
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