Question

A chord of length $14$ units subtends a $\angle {120}^{\circ }$ in a circle with radius $r=9$ units. What is the perimeter of the segment?

• A. $6\pi +12\mathrm{units}$
• B. $6\pi +14\mathrm{units}$
• C. $8\pi +12\mathrm{units}$
• D. $8\pi +14\mathrm{units}$

Answer 1

The correct option is B $6\pi +14\mathrm{units}$

Perimeter of the segment
$=\frac{\theta }{{360}^{\circ }}\times \pi d+l$
$=\frac{{120}^{\circ }}{{360}^{\circ }}\times \pi \times 18+14=6\pi +14$