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smaller arcs are equal

Source: 4-th Hong Kong Mathematical Olympiad 2001

February 16, 2007
geometrycircumcirclegeometry unsolved

Problem Statement

A triangle ABCABC is given. A circle Γ\Gamma, passing through AA, is tangent to side BCBC at point PP and intersects sides ABAB and ACAC at MM and NN respectively. Prove that the smaller arcs MPMP and NPNP of Γ\Gamma are equal iff Γ\Gamma is tangent to the circumcircle of ΔABC\Delta ABC at AA.
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