Let `A(0,6,6)`, B(6,6,0) and C(6,0,6) are three points and point D is moving on the line `x+z-3=0=y`. If G is centroid of `DeltaABC`, then minimum value of GD is

Options

A. `sqrt((47)/2)`
B. `sqrt((37)/2)`
C. `sqrt((57)/2)`
D. `sqrt((23)/2)`

Answer

C

Explanation

G=(4,4,4)
Let D=(a,0,3-a)
`GD^(2)=(a-4)^(2)+(0-4)^(2)+(3-a-4)^(2)`
`=2a^(2)-6a+33`.
For minimum of `GD^(2),a=3/2`
`GD_("min") = sqrt(2.9/4-6.3/2+33)=sqrt(57/2`