Apollonius theorem

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

If $b=c$ (the triangle is isosceles), then the theorem reduces to the Pythagorean theorem,

$$m^2+{(a/2)}^2=b^2.$$

Title	Apollonius theorem
Canonical name	ApolloniusTheorem
Date of creation	2013-03-22 11:44:10
Last modified on	2013-03-22 11:44:10
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	14
Author	yark (2760)
Entry type	Theorem
Classification	msc 51-00
Classification	msc 18-00
Classification	msc 81-00
Related topic	Triangle
Related topic	Median
Related topic	StewartsTheorem
Related topic	ProofOfStewartsTheorem
Related topic	ProofOfApolloniusTheorem2
Related topic	ParallelogramLaw
Related topic	ProofOfParallelogramLaw