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BM// AC, AB = BC, (ADC), (BDC)- All-Russian MO 1996 Regional (R4) 9.2

Source:

September 23, 2024
geometryisoscelesparalell

Problem Statement

In triangle ABCABC, in which AB=BCAB = BC, on side ABAB is selected point DD, and the ciscumcircles of triangles ADCADC and BDCBDC , S1S1 and S2S2 respectively. The tangent drawn to S1S_1 at point DD intersects S2S_2 for second time at point MM. Prove that BM∥ACBM \parallel AC.
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