1. 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°

2. 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.

3. 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.

4. 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°

5. O is the center of a circle. PQ is a diameter, and R is a point on the circumference. If \(\angle\)PQR = 40°, then what is the measure of \(\angle\)POR?

(a) 80° (b) 40° (c) 20° (d) 100°

6. 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.

7. 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 extended line BA at point T. If \(\angle PBO = 30^\circ\), then what is the measure of \(\angle PTA\)?

8. 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°

9. O is the center of a circle, and AB is its diameter. ABCD is a cyclic quadrilateral where AB\(\parallel\)DC, and \(\angle\)BAC = 75°. The value of \(\angle\)BCD will be-

(a) 60° (b) 45° (c) 75° (d) 50°

10. 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°

11. In a circle centered at \(O\), \(AB\) is a diameter. \(ABCD\) is a cyclic quadrilateral. If \(\angle ADC = 120^\circ\), then the measure of \(\angle BAC\) is –?

(a) 60° (b) 40° (c) 50° (d) 30°

12. 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.

13. 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.

14. “In the adjacent figure, O is the center of the circle and AC is the diameter. If ∠AOB = 80° and ∠ACE = 10°, then find the measure of ∠BED.”

15. “In the adjacent figure, O is the center of the circle and AB is the diameter. If ∠AOD = 140° and ∠CAB = 50°, then find the measure of ∠BED.”

16. 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?

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

(a) 50° (b) 200° (c) 80° (d) 180°

18. Two tangents are drawn to a circle from points A and B on the circumference, and they intersect at point C. Another point P lies on the circumference, on the side opposite to where point C is located with respect to the center. If \(\angle\)APB = 35°, then what is the measure of \(\angle\)ACB?

(a) 145° (b) 55° (c) 110° (d) None of the above

19. AB is a chord of a circle centered at O, and PT is a tangent to the circle at point A. If ∠ AOB = 120°, then what is the measure of ∠ BAT?

(a) 60° (b) 30° (c) 90° (d) 45°

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

21. In a circle with center O, PQ and PR are two chords. Tangents drawn at points Q and P intersect at point S. If ∠QSR = 70°, then what is the measure of ∠QPR?

22. In the adjacent figure, O is the center of the circle and AB is the diameter. Given that \(\angle\)AOD = 140° and \(\angle\)CAB = 50°, find the measure of \(\angle\)BED.

23. 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.

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

25. In a circle with center O, triangle ABC is inscribed. If \(\angle\)BAC = 85° and \(\angle\)BCA = 75°, then find the measure of \(\angle\)AOC.

26. Two tangents are drawn to a circle from points A and B on its circumference, and they intersect at point P. If \(\angle\)APB = 68°, then what is the measure of \(\angle\)PAB?

27. AB and CD are two chords of a circle with center O, and both have equal lengths. If \(\angle\)AOB = 60°, then what is the measure of \(\angle\)COD?

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

29. PQRS is a cyclic quadrilateral. PQ is the diameter of the circle, and if \(\angle\)PRS = 56°, then what is the value of \(\angle\)QPS?

30. 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.