Question

The radius of a circle is $9cms$. Find the length of an arc this circle which cuts off a chord of length equal to length of radius.

Answer 1

It is given that $OA=OB=AB=9cm$.

This gives that OAB is an equilateral triangle.

So, $\angle AOB={60}^{\circ }$.

The length of arc AB is,

$l=\frac{\theta }{360}\times 2\pi r$

$=\frac{60}{360}\times 2\pi \left(9\right)$

$=3\pi cm$

Hence answer is $3\pi cm.$