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The Sum of the Squares of the Distances from the Vertices to the Orthocenter
Let ABC be a triangle with orthocenter H and let
be the circumradius of ABC. Then:
AH
^{2}
+BH
^{2}
+CH
^{2}
=12
R
^{2}
-(AB
^{2}
+BC
^{2}
+AC
^{2}
)
Contributed by:
Jay Warendorff
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See Theorem 204 in N. Altshiller-Court,
College Geometry
, 2nd ed., Mineola, NY: Dover, 2007 p. 102.
RELATED LINKS
Circumradius
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Sum of the Squares of the Distances from the Vertices to the Orthocenter
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheSumOfTheSquaresOfTheDistancesFromTheVerticesToTheOrthocen/
Contributed by:
Jay Warendorff
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