Two circles of radii 4 cms and 1 cm touch each other externally and θ is

Question -

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

Options:

A .

\frac{24}{25}

B .

\frac{12}{25}

C .

\frac{3}{4}

D . none

Answer: Option A
:
A

$s i n \frac{θ}{2} = \frac{r_{1} - r_{2}}{r_{1} + r_{2}} = \frac{3}{5}, c o s \frac{θ}{2} = \frac{4}{5} s i n θ = \frac{24}{25}$

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