Question

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

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

Answer 1

The correct option is A $\frac{24}{25}$

From figure,
$\sin \frac{\theta }{2}=\frac{3}{5}$
and $\cos \frac{\theta }{2}=\frac{4}{5}$
$\therefore \sin \theta =2\cdot \frac{3}{5}\cdot \frac{4}{5}=\frac{24}{25}$