Question

In the given diagram, two circles pass through each other's centre. If the radius of each circle is 2, then what is the perimeter of the region marked B?

• A. $(\frac{8}{3})\pi$
• B. $(\frac{4}{5})\pi$
• C. $4\pi$
• D. $(\frac{5}{3})\pi$

Answer 1

Answer: (A)

$(\frac{8}{3})\pi$

Answer 2

Two circles with centers A and A' and having radius = 2 cm
$\angle BAC = 120^\circ \, \text{(since ABA' forms an equilateral triangle)} \, \text{and length of an arc} = \frac{\theta}{360^\circ} \times 2\pi r$
$\text{Perimeter of shaded portion} = 2 \times \left( \text{length of arc BC} \right)$
$= 2 \times \left( \frac{120^\circ}{360^\circ} \times 2\pi r \right)$
$= 2 \times \left( \frac{1}{3} \times 2\pi \times 2 \right)$
$= 2 \times \frac{4\pi}{3} = \frac{8\pi}{3}$
The correct answer is (A) : (8/3) π