Bisecting a Line Segment through the Orthocenter

HD

≈

2.45

DP'

≈

2.45

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.

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

Details

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

External Links

Triangle Centroid (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

Line Bisector (Wolfram MathWorld)

Orthocenter (Wolfram MathWorld)

Permanent Citation

Jay Warendorff

"Bisecting a Line Segment through the Orthocenter"
http://demonstrations.wolfram.com/BisectingALineSegmentThroughTheOrthocenter/
Wolfram Demonstrations Project
Published: March 7, 2011