Question

Prove Appolonius Theorem which states that in a triangle ABC \[{(AB)}^2+{(AC)}^2=2{(AD)}^2+{\frac 1 2}{(AD)}^2\] where D is the midpoint of BC.

Answer 1

Prove Appolonius Theorem which states that in a triangle ABC \[{(AB)}^2+{(AC)}^2=2{(AD)}^2+{\frac 1 2}{(AD)}^2\] where D is the midpoint of BC.

Answer 2

@ParthKohli @dan815 @nincompoop

Answer 3

Appolonius theorem is a special case of Stewart's theorem. You can find proof here :)

https://en.wikipedia.org/wiki/Stewart%27s_theorem