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AC=BC in A_1B_1C_1 with angle bisectors A1A, B1B, C_1C

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December 7, 2010
geometrycircumcirclegeometry unsolved

Problem Statement

Let A,B,CA,B,C be points on the sides B1C1,C1A1,A1B1B_1C_1, C_1A_1,A_1B_1 of a triangle A1B1C1A_1B_1C_1 such that A1A,B1B,C1CA_1A,B_1B,C_1C are the bisectors of angles of the triangle. We have that AC=BCAC = BC and A1C1≠B1C1.A_1C_1 \neq B_1C_1. (a)(a) Prove that C1C_1 lies on the circumcircle of the triangle ABCABC. (b)(b) Suppose that ∠BAC1=π6;\angle BAC_1 =\frac{\pi}{6}; find the form of triangle ABCABC.
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