1. ABCD is a cyclic quadrilateral, and O is the center of the circle. If ∠COD = 120° and ∠BAC = 30°, then ∠BOC and ∠BCD = _____.

2. ABCD is a cyclic quadrilateral and O is the center of the circle. If \(\angle\)COD = 120° and \(\angle\)BAC = 30°, then what is the measure of \(\angle\)BOC?

3. ABCD is a cyclic quadrilateral and O is the center of the circle. Given: \(\angle COD = 130^\circ\), \(\angle BAC = 25^\circ\) Find the values of \(\angle BOC\) and \(\angle BCD\).

(a) 40\(^o\),90\(^o\) (b) 50\(^o\),90\(^o\) (c) 65\(^o\),50\(^o\) (d) None of the above

4. In the cyclic quadrilateral ABCD, AB is the diameter and O is the center of the circle. If \(\angle\)ADC = 120°, then \(\angle\)BAC = _____

5. ABCD is a cyclic quadrilateral and O is the center of the circle. If \(\angle COD = 120^\circ\) and \(\angle BAC = 30^\circ\), then calculate the values of \(\angle BOC\) and \(\angle BCD\).

6. In the given figure, O is the center of the circle and AB is the diameter. ABCD is a cyclic quadrilateral. If ∠ADC = 120°, then find the measure of ∠BAC.

(a) 50° (b) 60° (c) 30° (d) 40°

7. ABCD is a cyclic quadrilateral where AB \(\parallel\) DC, and O is the center of the circle. Given: \(\angle\)BOC = 80°, and \(\angle\)ACO = 10° Find the measure of \(\angle\)BAD.

8. ABCD is a cyclic quadrilateral. The sides AD and AB are extended to E and F, respectively. If \(\angle\) CBF = 120°, then find the measure of \(\angle\) CDE.

9. In the adjacent figure, O is the center of the circle. Given: \(\angle\)OAB = 40°, \(\angle\)ABC = 120°, \(\angle\)BCO = y°, and \(\angle\)COA = x° Find the values of x and y.

10. PQRS is a cyclic quadrilateral, and the sides PQ and SR are extended to meet at point T. The center of the circle is O; if ∠POQ = 110°, ∠QOR = 60°, and ∠ROS = 80°, then calculate and write the values of ∠RQS and ∠QTR.

11. In the given figure, O is the center of the circle and AB is the diameter. ABCD is a cyclic quadrilateral. If ∠ABC = 65° and ∠DAC = 40°, then find the measure of ∠BCD.

(a) 75° (b) 105° (c) 115° (d) 80°

12. In a circle with center O, where BOC is the diameter and ABCD is a cyclic quadrilateral, if \(\angle ADC = 110^\circ\), then find the value of \(\angle ACB\).

13. The center of a circle is O, and AB is its diameter. ABCD is a cyclic quadrilateral. If \(\angle\)ABC = 65° and \(\angle\)DAC = 40°, then the measure of \(\angle\)BCD is—?

(a) 75° (b) 105° (c) 115° (d) 80°

14. In the cyclic quadrilateral ABCD, side AB is extended to point X. If ∠XBC = 82° and ∠ADB = 47°, then find the measure of ∠BAC.

15. ABCD is a cyclic quadrilateral. If BC is the diameter and ∠ADC = 130°, then what is the value of ∠ACB?

16. ABCD is a cyclic quadrilateral. The sides AB and DC are extended to meet at point P, and the sides AD and BC are extended to meet at point Q. If ∠ADC = 85° and ∠BPC = 40°, then find the measures of ∠BAD and ∠CQD.

17. In a circle centered at O, ABCD is a cyclic quadrilateral. Given: \(\angle ABD = 50^\circ\), \(\angle CAD = 28^\circ\), and \(\angle ADB = 32^\circ\) Find the measure of \(\angle BCD\).

(a) 72° (b) 52° (c) 62° (d) 82°

18. O is the center of the circle, and AB is its diameter. ABCD is a cyclic quadrilateral. Given that \(\angle\)ABC = 65° and \(\angle\)DAC = 60°, find the measure of \(\angle\)BCD.

19. In a circle centered at O, AB is a diameter. ABCD is a cyclic quadrilateral. Given \(\angle\)ABC = 65° and \(\angle\)DAC = 40°, find the value of \(\angle\)BCD.

20. ABCD is a cyclic quadrilateral. If \(\angle\)ABC = 65° and \(\angle\)CAD = 40°, then find the value of \(\angle\)BCD.

(a) 70° (b) 25° (c) 115° (d) 90°

21. ABCD is a cyclic quadrilateral. If \(\angle\) BAD = 65°, \(\angle\) ABD = 70°, and \(\angle\) BDC = 45°, then find the value of \(\angle\) ACB.

22. AOB is a diameter of the circle with center O, and C is a point on the circle. If \(\angle\)OBC = 60°, then find the measure of \(\angle\)OCA.

23. ABCD is a cyclic quadrilateral with O as the center of the circle. Side DC is extended up to point P. If \(\angle BCP = 108^\circ\), calculate and write the measure of \(\angle BOD\).

24. In the adjacent figure, O is the center of the circle. If \(\angle\)AEB = 110° and \(\angle\)CBE = 30°, find the value of \(\angle\)ADB.

(a) 70° (b) 60° (c) 80° (d) 90°

25. In the adjacent figure, O is the center of the circle, and BOA is the diameter. A tangent is drawn at point P on the circle, which intersects the extension of BA at point T. If ∠PBO = 30°, then find the measure of ∠PTA.

26. In the given figure, O is the center of the circle and AB is the diameter. ABCD is a cyclic quadrilateral where AB || DC and ∠BAC = 25°. Find the measure of ∠DAC.

27. In the adjacent figure, O is the center of the circle, and OP is perpendicular to AB. If AB = 6 cm and PC = 2 cm, then find the radius of the circle.

28. If ABCD is a cyclic quadrilateral and \(\angle\)A=120°, what is the measure of \(\angle\)C ?

(a) \(\cfrac{π}{3}\) (b) \(\cfrac{π}{6}\) (c) \(\cfrac{π}{2}\) (d) \(\cfrac{2π}{3}\)

29. In a circle with center \(O\), \(AB\) is the diameter, and \(P\) is a point on the circle. If \(\angle AOP = 104°\), find the value of \(\angle BPO\).

(a) 54° (b) 72° (c) 36° (d) 27°

30. If ABCD is a cyclic quadrilateral and ∠A = 100°, then the measure of ∠C is—?

(a) 50° (b) 200° (c) 80° (d) 180°