Bisecting a Line Segment through the Orthocenter

HD

≈

2.45

DP'

≈

2.45

A

B

C

P

G

H

P'

D

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.