IMO 1989 LL HKG32

Let ABC be an equilateral triangle. Let D, E, F, M, N, and

imolonglistmathematicsolympiad

IMO 1989 LL HKG32

Origin: HKG

Problem

Let ABC be an equilateral triangle. Let D, E, F, M, N, and P bee 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.