Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A
If `BC = 6, AC = 8`, then the length of side AB is equal to

Options

A. `(1)/(2)`
B. `(2)/(sqrt3)`
C. `5sqrt2`
D. none of these

Answer

C

Explanation

`FG xx FC = FA^(2)`
`rArr (1)/(3) (FC^(2)) = FA^(2)`
`rArr (2a^(2) + 2b^(2) -c^(2))/(3 xx4) = (c^(2))/(4)` (Using Apollonious theorem)
`rArr 2c^(2) = a^(2) + b^(2)`