1.

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

Answer»

`(1)/(2)`
`(2)/(SQRT3)`
`5sqrt2`
none of these

Solution :
`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)`


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