1. If an arc of a circle measuring 220 cm produces a central angle of 63°, find the radius of the circle.

2. The radius of a circle is 28 cm. Find the radian measure of the central angle subtended by an arc of length 5.5 cm.

3. If the radius of a circle is 7 cm, then find the radian measure of the central angle subtended by an arc of length 5.5 cm.

4. In a semicircle with a radius of 4 cm, AB is the diameter and ∠ACB is an angle inscribed in the semicircle. If BC = \(2\sqrt{7}\) cm, find the length of AC.

5. The radius of a circle is 28 cm. What is the circular measure of the central angle subtended by an arc of length 5.5 cm in that circle?

6. In a circle centered at O, the chords AB and CD are of equal length. If \(\angle\)AOB = 60° and CD = 6 cm, find the radius of the circle.

7. If the circle drawn by Shubho has a radius of 7 cm, then calculate and write the radian measure of the central angle subtended by an arc of length 5.5 cm on that circle.

8. The radius of a circle is 28 cm. In this circle, calculate and write the radian measure of the central angle subtended by an arc of length 5.5 cm.

9. If an arc of a circle measuring 44 cm produces a central angle of 45°, then what is the radius of the circle?

(a) 42 cm (b) 56 cm (c) 32 cm (d) 48 cm

10. Diameter PQ of a circle with radius 4 cm and angle ∠PRQ is an angle in the semicircle. Given QR = \(2\sqrt{7}\) cm, find the length of PR = _____

11. A horse runs along a circular path with a radius of 21 meters. In 5 seconds, it covers an arc that subtends a 60° angle at the center of the circle. Find the speed of the horse.

12. From point A, which is located 26 cm away from the center O of a circle, a tangent is drawn to the circle with a length of 10 cm. Find the radius of the circle.

13. Two parallel chords AB and CD of lengths 10 cm and 24 cm respectively lie on opposite sides of the center O of a circle. If the distance between the chords AB and CD is 17 cm, find the radius of the circle.

14. The radius of a circle is 28 cm. What is the radian measure of the central angle subtended by an arc of length 5.5 cm on this circle?

15. If the radius of a circle is 7 cm, then what will be the radian measure of the central angle subtended by an arc of length 5.5 cm?

16. In a circle centered at \(O\), two chords \(AB\) and \(CD\) have equal lengths. Given that \(\angle AOB = 60°\) and the radius of the circle is \(6\) cm, find the area of \(\triangle COD\).

(a) \(9\sqrt3\) square c.m (b) \(6\sqrt3\) square c.m (c) \(2\sqrt3\) square c.m (d) \(3\sqrt3\) square c.m

17. In a circle centered at O, the chords AB and CD are of equal length. If \(\angle\)AOB = 60° and CD = 6 cm, determine the radius of the circle.

18. Draw an isosceles triangle with a base length of 5.2 cm and each of the equal sides measuring 7 cm. Then, construct the circumcircle of the triangle and measure the circumradius. (Only mark the construction steps).

19. The length of a chord of a circle is 14 cm, and the perpendicular distance from the center to the chord is 24 cm. Find the radius of the circle.

20. Draw a triangle with a base length of 6.2 cm and the two adjacent angles measuring 50° and 75°; then construct its incircle. (Only provide the construction marks.)

21. Draw a triangle with side lengths of 7 cm, 6 cm, and 5.5 cm. Draw the incircle of the triangle and measure the radius of the incircle.

22. In a circle with a radius of 5 cm, AB and AC are two equal-length chords. The center of the circle lies outside triangle ABC. Given AB = AC = 6 cm, find the length of chord BC.

23. Draw a triangle where one side is 6.7 cm and the two adjacent angles are 75° and 55°. — Draw the triangle and then draw its circumcircle. Mark the position of the circumcenter and measure and write the length of the circumradius (i.e., the radius of the circumcircle). [Only drawing symbols required]

24. Triangle ABC where the base BC = 5 cm, ∠ABC = 100°, and AB = 4 cm. — Draw the triangle and then draw its circumcircle. Mark the position of the circumcenter and measure and write the length of the circumradius (i.e., the radius of the circumcircle). [Only drawing symbols required]

25. The lengths of two sides are 7.6 cm and 6 cm, and the included angle between them is 75°. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).

26. The length of one side is 6.2 cm, and the measures of the two angles adjacent to that side are 50° and 75°. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).

27. A right-angled triangle in which the two sides adjacent to the right angle are 7 cm and 9 cm. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).

28. A right-angled triangle in which the hypotenuse is 9 cm and one of the other sides is 5.5 cm. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).

29. An isosceles triangle where the base is 7.8 cm and each of the equal sides is 6.5 cm. — Draw the triangle and then draw its incircle. Measure and write the length of the inradius (i.e., the radius of the incircle).

30. In isosceles triangle ABC, the circumcenter is O and \(\angle ABC = 120^\circ\). If the radius of the circle is 5 cm, find the length of side AB.