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

Monjur Alahi

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


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Salim Ahmed Kawsar

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Correct Answer - 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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