# Bisection of Segments by the Sides of a Triangle

Bisection of Segments by the Sides of a Triangle

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''.