A Circumcircle through the Midpoint of a Triangle's Side

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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 (March 2011)
Open content licensed under CC BY-NC-SA


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