Question 73
Let $ABC$ be a triangle, let $B_1$ be the midpoint of the side $AB$ and $C_1$ the midpoint of the side $AC$. Let $P$ be the point of intersection, other than $A$, of the circumscribed circles around the triangles $ABC_1$ and $AB_1C$. Let $P_1$ be the point of intersection, other than $A$, of the line $AP$ with the circumscribed circle around the triangle $AB_1C_1$. Prove that $2AP = 3AP_1$.