If `A D` is the median of ` A B C ,` using vectors, prove that `A B^2+A C^2=2(A D^2+C D^2)dot`

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

A B C D is a rhombus. Prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

In Figure, prove that C D+D A+A B+B C >2A C

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^2

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2