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7922

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:
AH2+BH2+CH2=12R2-(AB2+BC2+AC2)

THINGS TO TRY

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DETAILS

See Theorem 204 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 102.

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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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