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A Concurrency from the Midpoints of Line Segments through the Circumcenter


	Let ABC be a triangle with circumcenter O. Let A', B', and C' be the perpendicular projections of A, B, and C onto BC, CA, and AB, respectively. Let , , and . Let A'', B'', and C'' be the midpoints of AD, BE, and CF, respectively. Then A'A'', B'B'', and C'C'' are concurrent.


	Contributed by: Jay Warendorff

Circumcenter (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

Concurrent (Wolfram MathWorld)

Midpoint (Wolfram MathWorld)

"A Concurrency from the Midpoints of Line Segments through the Circumcenter" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AConcurrencyFromTheMidpointsOfLineSegmentsThroughTheCircumce/

Contributed by: Jay Warendorff

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