Question

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

• A. $\frac{24}{25}$
• B. $\frac{12}{25}$
• C. $\frac{3}{4}$
• D. none

Answer 1

The correct option is A

$\frac{24}{25}$

$sin\frac{\theta }{2}=\frac{r_1-r_2}{r_1+r_2}=\frac{3}{5},cos\frac{\theta }{2}=\frac{4}{5}sin\theta =\frac{24}{25}$