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prove line tangent to circumcircle in triangle

Source: 2001 Moldova MO Grade 8 P3

April 12, 2021
geometry

Problem Statement

In a triangle ABCABC, the line symmetric to the median through AA with respect to the bisector of the angle at AA intersects BCBC at MM. Points PP on ABAB and QQ on ACAC are chosen such that MPACMP\parallel AC and MQABMQ\parallel AB. Prove that the circumcircle of the triangle MPQMPQ is tangent to the line BCBC.