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OM : OF : ON : OE : OP : OA

Source: IMO Longlist 1989, Problem 30

September 18, 2008
geometrygeometry unsolved

Problem Statement

Let ABC ABC be an equilateral triangle. Let D,E,F,M,N, D,E, F,M,N, and P P be the mid-points of BC,CA,AB,FD,FB, BC, CA, AB, FD, FB, and DC DC respectively. (a) Show that the line segments AM,EN, AM,EN, and FP FP are concurrent. (b) Let O O be the point of intersection of AM,EN, AM,EN, and FP. FP. Find OM:OF:ON:OE:OP:OA. OM : OF : ON : OE : OP : OA.
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