# Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 4

Areas related to Circles ncert solutions Chapter 12 Exercise 12.2 Question 4

4.     A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding: (i) minor segment   (ii) major segment. (Use $\pi=3.14$)

Solution:

AO = OB = 10 cm (Radii of circle)

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

Angle of sector for major sector is equal to $360-90 =270^\circ$

$\Rightarrow$ Area of major sector =Area shaded in light blue= $3.14 \times 10 \times 10 \times \frac{270^\circ}{360^\circ}=235.5$ $cm^2$

Area of minor segment=Area shaded in green

=Area of circle - area of major sector-Area of triangle $\triangle AOB$

$\Rightarrow$ Area of minor segment=$\pi.r^2-235.5-\frac{1}{2}.OA.OB$

$\Rightarrow$ Area of minor segment=$3.14 \times 10 \times 10-235.5-\frac{1}{2} \times 10 \times 10$

$=314-235.5-50=28.5$ $cm^2$

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