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prove that quadrilateral is cyclic and circle is tangent to lines

Source: 2001 Moldova MO Grade 10 P4

April 13, 2021
geometry

Problem Statement

In a triangle ABCABC, the angle bisector at AA intersects BCBC at DD. The tangents at DD to the circumcircles of the triangles ABDABD and ACDACD meet ACAC and ABAB at NN and MM, respectively. Prove that the quadrilateral AMDNAMDN is inscribed in a circle tangent to BCBC.