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Bisecting a Line Segment through the Orthocenter
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.
Contributed by:
Jay Warendorff
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See Problem 5 in N. Altshiller-Court,
College Geometry
, 2nd ed., Mineola, NY: Dover, 2007 p. 103.
RELATED LINKS
Triangle Centroid
(
Wolfram
MathWorld
)
Circumcircle
(
Wolfram
MathWorld
)
Line Bisector
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Bisecting a Line Segment through the Orthocenter
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BisectingALineSegmentThroughTheOrthocenter/
Contributed by:
Jay Warendorff
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