circle geometry - chords tangents angles subtended by chords, common tangents to circles - Question Bank
1. A chord subtends an angle of 180 degrees at the center. This chord is a:
2. Consider two circles with radii 6 cm and 4 cm. If they touch internally, what is the distance between their centers?
3. If two tangents are drawn from an external point to a circle, they are:
4. If a chord is equidistant from the center as another chord, then the lengths of the two chords are:
5. The angle subtended by a minor arc at the center is always:
6. When two circles are tangent externally, the distance between their centers is:
7. If a chord AB subtends an angle of 30 degrees at the circumference in the major segment, what is the angle subtended by the chord AB at the center?
8. What is the maximum number of common tangents that can be drawn to two circles of different radii that intersect each other?
9. If a line segment connects two points on a circle, it is a:
10. A chord is 12 cm long and its distance from the center is 8 cm. What is the radius of the circle?
11. If two circles intersect such that the distance between their centers is equal to the difference of their radii, they touch:
12. Consider a circle with center O and radius r. If a point P is outside the circle, and PA and PB are tangents to the circle at points A and B respectively, then:
13. If two circles touch externally at a point P, and AB is a common tangent, then angle APB is:
14. If a circle is inscribed in a square, what is the relationship between the diameter of the circle and the side of the square?
15. A tangent is drawn to a circle of radius 5 cm. What is the distance from the center to the point of contact?
16. In a circle, if two arcs are equal, then the corresponding chords are:
17. If a chord subtends an angle of 60 degrees at the circumference, what is the angle subtended by it at the center?
18. Two circles of radii 10 cm and 6 cm are 20 cm apart. How many common tangents can be drawn?
19. What is the relationship between the angle subtended by an arc at the center and the angle subtended by it at the circumference?
20. If two concentric circles have radii 7 cm and 3 cm, how many common tangents can be drawn?
21. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center.
22. If two circles touch internally, the number of direct common tangents is:
23. If two circles touch externally, the number of direct common tangents is:
24. Consider two circles with radii R and r (R > r). If the distance between their centers is d. For internal common tangents to exist, which condition must be met?
25. Consider two circles with radii R and r (R > r). If the distance between their centers is d. For external common tangents to exist, which condition must be met?
26. The angle in a semicircle is:
27. If two chords of a circle are equal in length, then they are:
28. In a circle, the angle subtended by an arc at the center is 120 degrees. The angle subtended by the same arc at any point on the circumference is:
29. Let a chord AB of a circle be at a distance of 5 cm from the center. If the radius of the circle is 13 cm, find the length of the chord AB.
30. If the distance between the centers of two circles is equal to the difference of their radii, they touch:
31. If the distance between the centers of two circles is equal to the sum of their radii, they touch:
32. Two circles have radii 5 cm and 2 cm. If the distance between their centers is 10 cm, how many common tangents can be drawn?
33. The distance between the centers of two circles is 13 cm and their radii are 8 cm and 3 cm. What type of tangents do they have?
34. Two parallel tangents to a circle are always:
35. If a chord is perpendicular to a diameter, the diameter:
36. A line that intersects a circle at two points is called a:
37. What is the longest possible chord in a circle?
38. A line segment joining the center of a circle to any point on its circumference is called a:
39. The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the:
40. If two circles intersect at two distinct points, the number of common tangents is:
41. If two circles are completely separate (do not intersect), the number of common tangents is:
42. If two circles touch each other internally, the number of common tangents is:
43. If two circles touch each other externally, the number of common tangents is:
44. Angles subtended by the same arc at the circumference are:
45. The angle subtended by a diameter at any point on the circumference is:
46. If a chord passes through the center of a circle, it is called a:
47. What is the angle between a tangent and the radius at the point of contact?
48. A tangent to a circle is a line that:
49. What is the definition of a chord in a circle?