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Three Subtriangles of a Triangle

A cevian is a line drawn from a vertex of a triangle to the opposite side.
Let ABC be a triangle. Let BB' and CC' be cevians. Let M and N be the midpoints of BB' and CC' respectively. Let R and S be the points of intersection of AM and AN with C'B'. Then .

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The statement of the theorem is in Problem 89. Triangle area, Midpoints.

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"Three Subtriangles of a Triangle" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ThreeSubtrianglesOfATriangle/
Contributed by: Jay Warendorff
After work by: Antonio Gutierrez
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