IMO 1972 LL NET29

Let A, B, C be points on the sides B1C1, C1A1, A1B1 of a

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IMO 1972 LL NET29

Origin: NET

Problem

Let A, B, C be points on the sides B1C1, C1A1, A1B1 of a triangle A1B1C1 such that A1A, B1B, C1C are the bisectors of angles of the triangle. We have that AC = BC and A1C1 ̸= B1C1. (a) Prove that C1 lies on the circumcircle of the triangle ABC. (b) Suppose that ∡BAC1 = \pi/6; find the form of triangle ABC.