Let P be a fixed point on side BC of ΔABC and define set PAIRS by

   { (X,Y) | X on side AC, Y on side AB, and ∠PXC = ∠PYB }.

Prove that the midpoints of line segments XY for all pairs (X,Y) ∈ PAIRS lie on a straight line.

Note: For this problem, a point on a side of ΔABC excludes the vertices.

   

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