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Two Triangles of Equal Area on Either Side of an Angle Bisector


	Let ABC be a triangle and let the angle bisector at vertex C intersect the circumcircle at R and the perpendicular bisectors of BC and AC at P and Q, respectively. Let the midpoints of BC and AC be S and T, respectively. Then RQT and RPS have equal area.


	Contributed by: Jay Warendorff

See IMO 2007 shortlist geometry problem G1.

Angle Bisector (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

"Two Triangles of Equal Area on Either Side of an Angle Bisector" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TwoTrianglesOfEqualAreaOnEitherSideOfAnAngleBisector/

Contributed by: Jay Warendorff

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