Question

The radius of a circle is $12$ cm. If a chord of length $12$ cm is drawn then find the area of the smaller segment.

Answer 1

Let AB be the chord and O be the centre of the circle
$OA=OB=AB=12$ cm
$\therefore$ OAB is an equilateral triangle and
$<AOB={60}^{\circ }$
Area of smaller segment = Area of sector AOB - Area of triangle AOB

$=\frac{60}{360}\times \pi {\left(12\right)}^2-\frac{\sqrt{3}}{4}{\left(12\right)}^2$

$=(24\pi -36\sqrt{3})$ sq units