Alternate Segment Theorem

Q.

In a circle of radius $21\mathrm{cm}$, an arc subtends an angle of $60°$ at the center. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord

Q.

$ABC$ is a triangle with $\angle A=30°$, $BC=10$cm. The area of the circumcircle of the triangle is

1. $100\pi$ sq cm

2. $5$ sq cm

3. $25$ sq cm

4. $100\frac{\pi }{3}$ sq cm

Q.

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord.

1. 2

2. 1.5

3. 3

4. None of these