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Indian RMO - Paper 3

Source: RMO- Problem 5

December 11, 2013
geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

Let ABCABC be a triangle which it not right-angled. De fine a sequence of triangles AiBiCiA_iB_iC_i, with i≥0i \ge 0, as follows: A0B0C0A_0B_0C_0 is the triangle ABCABC and, for i≥0i \ge 0, Ai+1,Bi+1,Ci+1A_{i+1},B_{i+1},C_{i+1} are the reflections of the orthocentre of triangle AiBiCiA_iB_iC_i in the sides BiCiB_iC_i,CiAiC_iA_i,AiBiA_iB_i, respectively. Assume that ∠Am=∠An\angle A_m = \angle A_n for some distinct natural numbers m,nm,n. Prove that ∠A=60∘\angle A = 60^{\circ}.
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