Hi, i am having trouble with this proof. I have found mulitple webpages on the theorem, but not one of them i coudl find offers me a 'how to'

It is to do with Appolonis' Theorem. The question is:

"In triangle ABC, D is the midpoint of BC, then prove that -

AB² + AC² = 2AD² + 2CD²

Hint:Use Pythagoras' Theorem."

although from looking at the web, i am thinking my teacher has copied it down incorrectly since they all seem to say AB² + AC² = 2AD² + (BC²)/2

since AD is a median, and it is not known that there are any right angles in this triangle, i am not sure how to get Pythagoras in there at all

thanks for any help

jacs