PlanetMath: Apollonius theorem

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Apollonius theorem

(Theorem)

Let the sides of a triangle and the length of the median to the side with length . Then $b^2+c^2=2m^2+\frac{a^2}{2}$ .

$\includegraphics{apollonius}$

If (the triangle is isosceles), then the theorem reduces to the Pythagorean theorem,

$\displaystyle m^2 + (a/2)^2 = b^2.$

"Apollonius theorem" is owned by yark. [ full author list (3) | owner history (2) ]

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Keywords:

Triangle, median

Attachments:: proof of Apollonius theorem (Proof) by quincynoodles
proof of Apollonius theorem (Proof) by drini
lengths of triangle medians (Corollary) by pahio

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Cross-references: Pythagorean theorem, isosceles, median, triangle, sides
There are 3 references to this entry.

This is version 6 of Apollonius theorem, born on 2001-10-06, modified 2006-02-13.
Object id is 146, canonical name is ApolloniusTheorem.
Accessed 13957 times total.

Classification:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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