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Two circles of radii 4 cm and 1 cm touch each other externally and $θ$ is the angle contained by their direct common tangents. Then $\sin θ$ is equal to

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24/25

12/25

3/4

3/5

answer is A.

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Detailed Solution

$\begin{array}{l} \sin \frac{θ}{2} = \frac{3}{5} \\ A n d \cos \frac{θ}{2} = \frac{4}{5} \\ ∴ \sin θ = 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25} \end{array}$

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