Let $ABC$ be an acute triangle. Let $M_A, M_B$ and $M_C$ be the midpoints of sides $BC,CA$, respectively $AB$. Let $M'_A , M'_B$ and $M'_C$ be the the midpoints of the arcs $BC, CA$ and $AB$ respectively of the circumscriberd circle of triangle $ABC$. Let $P_A$ be the intersection of the straight line $M_BM_C$ and the perpendicular to $M'_BM'_C$ through $A$. Define $P_B$ and $P_C$ similarly. Show that the straight line $M_AP_A, M_BP_B$ and $M_CP_C$ intersect at one point.