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

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 . 2425

B . 1225

C . 34

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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