Question

The angle between the legs of a compass of ${60}^{\circ }$ and each leg is $10cm$ long. How far apart are the points on which the legs of the compass rest?

• A. $5cm$
• B. $10cm$
• C. $5\sqrt{3}cm$
• D. $10\sqrt{3}cm$

Answer 1

The correct option is B $10cm$

R.E.F image

As $OA=OB$

$\Rightarrow \angle A=\angle B$

& $\angle A+\angle B+{60}^{\circ }={180}^{\circ }$

$\Rightarrow \angle A=\angle B={60}^{\circ }$

$\therefore \Delta AOB$ is equilateral

$\Rightarrow AB=10cm$