circle geometry - chords tangents angles subtended by chords, common tangents to circles - One Line Questions

1. If two circles intersect at two distinct points, the number of common tangents is: — 2
2. If two circles touch externally, the number of direct common tangents is: — 2
3. If two circles touch internally, the number of direct common tangents is: — 1
4. If two concentric circles have radii 7 cm and 3 cm, how many common tangents can be drawn? — 0
5. What is the maximum number of common tangents that can be drawn to two circles of different radii that intersect each other? — 2
6. A tangent is drawn to a circle of radius 5 cm. What is the distance from the center to the point of contact? — 5 cm
7. What is the angle between a tangent and the radius at the point of contact? — 90 degrees
8. If two circles touch each other externally, the number of common tangents is: — 3
9. If two circles touch each other internally, the number of common tangents is: — 1
10. If two circles are completely separate (do not intersect), the number of common tangents is: — 4
11. 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? — 4
12. Two circles of radii 10 cm and 6 cm are 20 cm apart. How many common tangents can be drawn? — 4
13. 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. — 24 cm
14. 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? — 60 degrees
15. Consider two circles with radii 6 cm and 4 cm. If they touch internally, what is the distance between their centers? — 2 cm
16. 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: — 60 degrees
17. If a chord subtends an angle of 60 degrees at the circumference, what is the angle subtended by it at the center? — 120 degrees
18. The angle subtended by a diameter at any point on the circumference is: — 90 degrees
19. If two circles touch externally at a point P, and AB is a common tangent, then angle APB is: — 90 degrees
20. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center. — 6 cm
21. A chord is 12 cm long and its distance from the center is 8 cm. What is the radius of the circle? — 10 cm
22. What is the definition of a chord in a circle? — A line segment whose endpoints both lie on the circle.
23. The angle in a semicircle is: — Right
24. The angle subtended by a minor arc at the center is always: — Acute
25. Angles subtended by the same arc at the circumference are: — Always equal
26. What is the relationship between the angle subtended by an arc at the center and the angle subtended by it at the circumference? — Angle at center is double the angle at circumference.
27. If a chord is perpendicular to a diameter, the diameter: — Both A and B
28. The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the: — Circumference
29. A line segment joining the center of a circle to any point on its circumference is called a: — Radius
30. 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? — d > R + r
31. 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? — d > R + r
32. If a circle is inscribed in a square, what is the relationship between the diameter of the circle and the side of the square? — Diameter is equal to the side
33. Two parallel tangents to a circle are always: — Both A and B
34. If the distance between the centers of two circles is equal to the difference of their radii, they touch: — Internally
35. If two circles intersect such that the distance between their centers is equal to the difference of their radii, they touch: — Internally
36. If a chord is equidistant from the center as another chord, then the lengths of the two chords are: — Equal
37. If the distance between the centers of two circles is equal to the sum of their radii, they touch: — Externally
38. A tangent to a circle is a line that: — Intersects the circle at exactly one point.
39. 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? — No common tangents
40. 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: — All of the above
41. If two chords of a circle are equal in length, then they are: — Equidistant from the center
42. In a circle, if two arcs are equal, then the corresponding chords are: — Equal
43. If two tangents are drawn from an external point to a circle, they are: — Equal in length
44. What is the longest possible chord in a circle? — Diameter
45. A chord subtends an angle of 180 degrees at the center. This chord is a: — Diameter
46. If a chord passes through the center of a circle, it is called a: — Diameter
47. A line that intersects a circle at two points is called a: — Secant
48. If a line segment connects two points on a circle, it is a: — Chord
49. When two circles are tangent externally, the distance between their centers is: — The sum of their radii
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