In `DeltaABC` the mid points of the sides AB, BC and CA are `(l, 0, 0), (0, m, 0) and (0, 0,n)` respectively. Then, `(AB^2+BC^2+CA^2)/(l^2+m^2+n^2)` is equal to

Options

A. `2`
B. `4`
C. `8`
D. `16`

Answer

C

Explanation

From the figure
`x_1+x_2=2l,y_1+y_2=0,z_1+z_2=0`
`x_2+x_3=0,y_2+y_3=2m,z_2+z_3=0`
`and x_1+x_3=0,y_1+y_3=0,z_1+z_3=2n`
On solving, we get the coordinates are A(l,-m,n),
`therefore(AB^2+BC^2+CA^2)/(l^2+m^2+n^2)=((4m^2+4n^2)+(4l^2+4n^2)+(4l^2+4m^2))/(l^2+m^2+n^2)`
`=(8(l^2+m^2+n^2))/(l^2+m^2+n^2)=8`