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BD tangent to (O_1O_2A), AB=BC - All-Russian MO 1997 Regional (R4) 10.7

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September 24, 2024
geometrytangentisosceles

Problem Statement

Points O1O_1 and O2O_2 are the centers of the circumscribed and inscribed circles of an isosceles triangle ABCABC (AB=BCAB = BC). The circumcircles of triangles ABCABC and O1O2AO_1O_2A intersect at points AA and DD. Prove that line BDBD is tangent to the circumcircle of the triangle O1O2AO_1O_2A.
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