ILL 1989 Problem 30

Let $ABC$ be an equilateral triangle. Let $D,E, F,M,N,$ and $P$ be the mid-points of $BC, CA, AB, FD, FB,$ and $DC$ respectively.

(a) Show that the line segments $AM,EN,$ and $FP$ are concurrent. (b) Let $O$ be the point of intersection of $AM,EN,$ and $FP.$ Find $OM : OF : ON : OE : OP : OA.$