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A Circumcircle through the Midpoint of a Triangle's Side


	Let ABC be a triangle. Let the feet of the altitudes from A, B, and C be A', B' and C', respectively. Let the line through A' parallel to B'C' meet AC and AB at Q and R, respectively. Let the line B'C' meet BC at P. Then the circumcircle of PQR passes through the midpoint M of BC.


	Contributed by: Jay Warendorff

See Circumcircle of triangle PQR passes through midpoint of BC, IMO Shortlist 1997, Q18.

Altitude (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

Midpoint (Wolfram MathWorld)

Parallel (Wolfram MathWorld)

"A Circumcircle through the Midpoint of a Triangle's Side" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ACircumcircleThroughTheMidpointOfATrianglesSide/

Contributed by: Jay Warendorff

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