Problem #PRU-116087

Problem

Three circles are constructed on a triangle, with the medians of the triangle forming the diameters of the circles. It is known that each pair of circles intersects. Let $C_1$ be the point of intersection, further from the vertex $C$, of the circles constructed from the medians $A{M}_1$ and $B{M}_2$. Points $A_1$ and $B_1$ are defined similarly. Prove that the lines $A{A}_1$, $B{B}_1$ and $C{C}_1$ intersect at the same point.