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Line Segments through the Vertices and the Circumcenter of an Acute Triangle


	Let ABC be an acute triangle, O its circumcenter, and R its circumradius. Let D, E, and F be the points along AO, BO, and CO across from A, B, and C. Then .


	Contributed by: Jay Warendorff

See the First Iberoamerican Olympiad (problem 6).

Acute Triangle (Wolfram MathWorld)

Circumcenter (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

"Line Segments through the Vertices and the Circumcenter of an Acute Triangle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/LineSegmentsThroughTheVerticesAndTheCircumcenterOfAnAcuteTri/

Contributed by: Jay Warendorff

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