1. The central angle subtended by an arc of a circle is twice the inscribed angle subtended by the same arc—prove it.

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

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

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

5. The central angle subtended by an arc of a circle is twice any inscribed angle subtended by the same arc.

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

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

8. Prove that the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circumference.

9. Prove that the angle subtended at the center by an arc of a circle is twice the angle subtended by the same arc at any point on the circle.

10. 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.

11. Prove that the central angle subtended by the same arc is twice the inscribed angle.

12. 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°.

13. An inscribed angle subtended by the same arc is half of the central angle subtended by that arc.

14. The measure of all inscribed angles subtended by the same arc in a circle is equal.

15. Prove that the angle subtended at the center of any circle by an arc is double the angle subtended by the same arc at any point on the remaining part of the circle.

16. Prove that the angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the remaining part of the circumference.

17. AB is the diameter of a circle with center O. A straight line drawn from point A intersects the circle at point C, and the tangent drawn from point B intersects this line at point D. Prove that: For any such straight line, the area of the rectangle formed by AC and AD is always constant.

18. 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?

19. Prove that the quadrilateral formed by the intersection of the angle bisectors of the four angles of any quadrilateral is a cyclic quadrilateral.

20. 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?

21. 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.

22. 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?

23. 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?

24. 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.

25. If the angle formed between two intersecting chords of a circle is bisected by a line that passes through the center, then prove that the two chords are equal.

26. 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.

27. "Prove that, in any cyclic quadrilateral, the two central angles formed by any pair of opposite sides are supplementary."

28. 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.

29. The angle formed between the two tangents drawn from an external point to a circle is bisected by the straight line segment connecting that point to the center of the circle.

30. Prove that all angles subtended by the same arc of a circle are equal.