Question

A chord of a circle of radius $10cm$ subtends a right angle at the centre, then the area of the minor segment is

• A. $78.5c{m}^2$
• B. $28.5c{m}^2$
• C. $50c{m}^2$
• D. $128.5c{m}^2$

Answer 1

The correct option is B

$28.5c{m}^2$

Find the area of minor segment

Given,
$OA=OB=10cm$

Central angle $=\theta =90°$

$\text{Area of segment APB = Area of sector OAPB – Area of △AOB}$

$$\begin{gathered} =\frac{\theta }{360°}\times \pi r^2–\frac{1}{2}\times OA\times OB \\ =\frac{{90}^{°}}{360°}\times 3.14\times 10\times 10–\frac{1}{2}\times 10\times 10 \\ =\frac{314}{4}–50 \\ =78.5–50 \\ =28.5c{m}^2 \end{gathered}$$

Hence, the correct option is B