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Two tangents meet on BC

Source: 2018 RMM Shortlist G2

February 21, 2019
geometry

Problem Statement

Let △ABC\triangle ABC be a triangle, and let SS and TT be the midpoints of the sides BCBC and CACA, respectively. Suppose MM is the midpoint of the segment STST and the circle ω\omega through A,MA, M and TT meets the line ABAB again at NN. The tangents of ω\omega at MM and NN meet at PP. Prove that PP lies on BCBC if and only if the triangle ABCABC is isosceles with apex at AA.
Proposed by Reza Kumara, Indonesia
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