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ASU 474 All Soviet Union MO 1988 find M which minimises MP

Source:

August 8, 2019
minimumgeometrycircumcircle

Problem Statement

In the triangle ABCABC, ∠C\angle C is obtuse and DD is a fixed point on the side BCBC, different from BB and CC. For any point MM on the side BCBC, different from DD, the ray AMAM intersects the circumcircle SS of ABCABC at NN. The circle through M,DM, D and NN meets SS again at PP, different from NN. Find the location of the point MM which minimises MPMP.
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