Question 123
Either $ABC$ a triangle, or $O$ the center of its circumscribed circle. Let $I$ be the center of the circle inscribed in the triangle $ABC$ and $D$ the point of tangency of this circle with the segment $[AC]$. The straight lines $(OI)$ and $(AB)$ intersect at a point $P$. Let $M$ be the middle of the arc $AC$ not containing $B$ and $N$ the arc medium $BC$ containing $A$. Show that the straight lines $(MD)$ and $(NP)$ intersect on the circle circumscribed at $ABC$.