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<COA = <B + 60^o, 3 times - All-Russian MO 1996 Regional (R4) 11.7

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September 23, 2024
geometryanglessimilar triangles

Problem Statement

In triangle ABCABC, a point OO is taken such that ∠COA=∠B+60o\angle COA = \angle B + 60^o, ∠COB=∠A+60o\angle COB = \angle A + 60^o, ∠AOB=∠C+60o\angle AOB = \angle C + 60^o.Prove that if a triangle can be formed from the segments AOAO, BOBO, COCO, then a triangle can also be formed from the altitudes of triangle ABCABC and these triangles are similar.
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