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point symmetric of vertex wrt line connecting feet of bisectors lies on side

Source: Russian Regional Olympiad 2010 9.4

August 24, 2024
geometrysymmetry

Problem Statement

In triangle ABCABC, ∠A=60o\angle A =60^o. Let BB1BB_1 and CC1CC_1 be angle bisectors of this triangle. Prove that the point symmetrical to vertex AA with respect to line B1C1B_1C_1 lies on side BCBC.
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