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Let G be the centroid of triangle ABC an...

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A
If `angleGAC = (pi)/(3) and a = 3b`, then sin C is equal to

A

`(3)/(4)`

B

`(1)/(2)`

C

`(2)/(sqrt3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
In `DeltaADC`, we have,
`(a//2)/(sin (pi//3)) = (AD)/(sin C) rArr sin C = (sqrt3)/(2a) sqrt(2b^(2) + 2c^(2) -a^(2))`
`=(sqrt3)/(2a) sqrt(3b^(2)) = (3)/(2) (b)/(a) = (1)/(2)`
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