Concurrency via Midpoints

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Let ABC be a triangle and P be an internal point. Let AP, BP, and CP intersect the sides BC, CA, and AB in A', B', and C'. Let L, M, and N be the midpoints of the sides of ABC and L', M', and N' be the midpoints of the sides of A'B'C'. Then LL', MM', and NN' are concurrent.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA



See problem 20 in Classical Theorems in Plane Geometry.

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