Let ABC be a triangle with AB = 26, AC = 28, BC = 30. Let X, Y , Z be the midpoints of arcs BC,
CA, AB (not containing the opposite vertices) respectively on the circumcircle of ABC. Let P be the
midpoint of arc BC containing point A. Suppose lines BP and XZ meet at M , while lines CP and
XY meet at N. Find the square of the distance from X to MN.

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