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 Median length, Apollonius' Theorem

The following theorem has been attributed to Apollonius of Perga: In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side. In other words, if BM is a median of a triangle ABC and if AB = c, BC = a, AC = b, and BM = m, prove that Median length equation.

Median Length theorem

See also:
Pythagoras Theorem
Euclid's Elements Book II Proposition 13
Stewart Theorem

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Aug 23, 2014