1. 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?

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 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.

4. 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?

5. If the radius of a circle is 6 cm, calculate and write the radian measure of the central angle subtended at the center by an arc of length 15 cm.

6. 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.

7. 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?

8. The diameter of a circle is 28 cm. What is the radian measure of the central angle subtended by an arc of length 5.5 cm?

9. The measure of the central angle formed at the center of a circle by an arc whose length is equal to the radius of the circle is 1 radian.

10. 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).

11. 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.

12. 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).

13. 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).

14. 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).

15. 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).

16. 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.

17. If the central angle of a circle centered at point O is 300°, then the angle subtended at the circumference by the same arc will be 60°.

18. 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]

19. 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]

20. 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).

21. Draw an equilateral triangle with side length 7 cm. Then draw both the circumcircle and the incircle of the triangle. Using a scale, determine the lengths of the circumradius and the inradius. Also, write whether there is any relationship between them.

22. In a circle, two arcs of unequal length subtend angles at the center in the ratio 5:2. If the sexagesimal (degree) measure of the second angle is 30°, then calculate and write both the sexagesimal and radian measures of the first angle.

23. 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 = _____

24. In a circle, two arcs of unequal lengths are in the ratio 5:2. If the central angle corresponding to the second arc is 30°, what is the radian measure of the central angle corresponding to the first arc?

25. Two circles touch each other externally. The distance between their centers is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle is —

(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm

26. Two identical circles, each with a radius of 10 cm, intersect each other, and the length of their common chord is 12 cm. Find the distance between the centers of the two circles.

27. 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.

28. Point P is any point inside a circle centered at O. If the radius of the circle is 5 cm and OP = 3 cm, then find the minimum length of the chord passing through point P.

29. If an arc of a circle measuring 220 cm in length subtends a central angle of 60°, find the radius of the circle.

30. Prove that the central angle subtended by an arc of a circle is twice any inscribed angle subtended by the same arc.