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Bisecting a Line Segment through the Orthocenter

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Let P and P' be opposite points on the circumcircle of the triangle ABC. Let G be the centroid of ABC and H its orthocenter. Then PG bisects HP' at D.

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Drag the purple points A, B, C, or P to change the figure.

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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See Problem 5 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 103.

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