# Bisection of Segments by the Sides of a Triangle

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Let ABC be a triangle with orthocenter H, and let the feet of the altitudes be A', B' and C'. Let the extensions of the altitudes intersect the circumcircle a second time at A'', B'', and C''. Then HA' = A' A'', HB' = B' B'', and HC' = C' C''.

Contributed by: Jay Warendorff (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

See Theorem 178 in N. Altshiller-Court, *College Geometry*, 2nd ed., Mineola, NY: Dover, 2007 p. 95.

## Permanent Citation

"Bisection of Segments by the Sides of a Triangle"

http://demonstrations.wolfram.com/BisectionOfSegmentsByTheSidesOfATriangle/

Wolfram Demonstrations Project

Published: March 7 2011