The exinscribed circle of a triangle ABC corresponding to its vertex A touches the sidelines AB and AC in the points M and P, respectively, and touches its side BC in the point N. Show that if the midpoint of the segment MP lies on the circumcircle of triangle ABC, then the points O, N, I are collinear, where I is the incenter and O is the circumcenter of triangle ABC. geometrycircumcircleincentertrigonometrygeometric transformationreflectionparallelogram