The `A D ,B Ea n dC F` are the medians of a c` A B C ,` then `(A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2)` is equal to

If AD, BE and CF are the medians of a DeltaA B C ,t h e n(A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2) is equal to

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 Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a)C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

If E is a point on side C A of an equilateral triangle A B C such that B E_|_C A , then A B^2+B C^2+C A^2= 2 B E^2 (b) 3 B E^2 (c) 4 B E^2 (d) 6 B E^2

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then(a^2)/8 is equal to (a)m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c)m_1^2+m_3^2-2m_2^2 (d) none of these

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F