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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 .

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See the First Iberoamerican Olympiad (problem 6).

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"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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