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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''.
Contributed by:
Jay Warendorff
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See Theorem 178 in N. Altshiller-Court,
College Geometry
, 2nd ed., Mineola, NY: Dover, 2007 p. 95.
RELATED LINKS
Altitude
(
Wolfram
MathWorld
)
Circumcircle
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Bisection of Segments by the Sides of a Triangle
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BisectionOfSegmentsByTheSidesOfATriangle/
Contributed by:
Jay Warendorff
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