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Bisectors in triangle

Source: Moldova TST, day 2, problem 3

March 8, 2011
geometryincentergeometry unsolved

Problem Statement

Let ABCABC be a triangle with ∠BAC=60\angle BAC=60. Let B1B_1 and C1C_1 be the feet of the bisectors from BB and CC. Let A1A_1 be the symmetrical of AA according to line B1C1B_1C_1. Prove that A1,B,CA_1, B, C are colinear.
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