A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segments (given, π=3.14 ) is

Correct option is C

Given: A chord of a circle of radius 10 cm subtends a right angle at the centre. given, π = 3.14 ) 

Formula used:

Area of Sector $$= \frac{\theta}{360^\circ} \times \pi r^2$$

Area of Triangle $$= \frac{1}{2} \times \text{Base} \times \text{Height}$$​

Solution:

Let AB be the chord of a circle subtending an angle of $$90^\circ$$​at the centre O of the circle.

Area of Sector =$$\frac{90^\circ}{360^\circ} \times 3.14 \times (10)^2$$​​
Area of Sector = $$\frac{1}{4} \times 3.14 \times 100$$​
​Area of Sector = $$78.5 \text{ cm}^2$$

Corresponding minor segment = $$\triangle AOB$$​

Area of Triangle = $$\frac{1}{2} \times 10 \times 10$$​
Area of Triangle ​$$= 50 \text{ cm}^2$$​​

Area of Minor Segment = Area of Sector − Area of Triangle

Area of Minor Segment =78.5 − 50

Area of Minor Segment = 2$$8.5 \text{ cm}^2$$

Thus, the correct answer is (c).