MathDB
tangent circumcircles starting with a semicircle and two altitudes

Source: Sharygin 2011 Final 9.1

December 16, 2018
geometrycircumcircletangent circlesaltitudessemicircle

Problem Statement

Altitudes AA1AA_1 and BB1BB_1 of triangle ABC meet in point HH. Line CHCH meets the semicircle with diameter ABAB, passing through A1,B1A_1, B_1, in point DD. Segments ADAD and BB1BB_1 meet in point MM, segments BDBD and AA1AA_1 meet in point NN. Prove that the circumcircles of triangles B1DMB_1DM and A1DNA_1DN touch.
Back to ProblemsView on AoPS