MATHEMATICS CLASS- 10
MCQ- CH-10(Circles)
Class 10 Mathematics
Chapter 10: Circles
50 Board-Level MCQs with Answers and Solutions
Q1. The tangent to a circle at any point is
(a) Parallel to the radius
(b) Perpendicular to the radius through the point of contact
(c) Equal to the radius
(d) A diameter
Answer: (b) Perpendicular to the radius through the point of contact
Q2. A tangent intersects a circle at
(a) Two points
(b) Three points
(c) One point
(d) No point
Answer: (c) One point
Q3. The common point of a tangent and a circle is called
(a) Centre
(b) Chord
(c) Point of Contact
(d) Radius
Answer: (c) Point of Contact
Q4. How many tangents can be drawn at a point on a circle?
(a) One
(b) Two
(c) Three
(d) Infinite
Answer: (a) One
Q5. The angle between a tangent and the radius through the point of contact is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer: (d) 90°
Q6. The number of tangents that can be drawn from an external point to a circle is
(a) 1
(b) 2
(c) 3
(d) Infinite
Answer: (b) 2
Q7. Tangents drawn from an external point to a circle are
(a) Unequal
(b) Perpendicular
(c) Equal in length
(d) Parallel
Answer: (c) Equal in length
Q8. If PA and PB are tangents from external point P, then
(a) PA > PB
(b) PA < PB
(c) PA = PB
(d) PA + PB = 0
Answer: (c) PA = PB
Q9. A line which cuts a circle at two distinct points is called
(a) Tangent
(b) Radius
(c) Secant
(d) Diameter
Answer: (c) Secant
Q10. The longest chord of a circle is
(a) Radius
(b) Tangent
(c) Diameter
(d) Arc
Answer: (c) Diameter
Q11. A tangent to a circle and the radius through the point of contact are
(a) Parallel
(b) Perpendicular
(c) Equal
(d) Coincident
Answer: (b)
Q12. If radius of a circle is 5 cm, then diameter is
(a) 5 cm
(b) 7 cm
(c) 10 cm
(d) 15 cm
Answer: (c) 10 cm
Q13. The point from which two tangents are drawn lies
(a) Inside the circle
(b) On the circle
(c) Outside the circle
(d) At the centre
Answer: (c)
Q14. If PA and PB are tangents from P and PA = 8 cm, then PB =
(a) 4 cm
(b) 8 cm
(c) 12 cm
(d) 16 cm
Answer: (b)
Q15. A tangent and a secant differ because
(a) Tangent touches at one point, secant cuts at two points
(b) Both touch at one point
(c) Both cut at two points
(d) Tangent passes through centre
Answer: (a)
Q16. How many tangents can be drawn from a point on the circle?
(a) 0
(b) 1
(c) 2
(d) Infinite
Answer: (b)
Q17. The centre of a circle lies on the
(a) Radius drawn to point of contact
(b) Tangent
(c) Arc
(d) Chord
Answer: (a)
Q18. If O is centre and PT is tangent at T, then ∠OTP equals
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer: (d)
Q19. A circle can have how many tangents?
(a) One
(b) Two
(c) Four
(d) Infinite
Answer: (d)
Q20. If radius = 7 cm, diameter =
(a) 7 cm
(b) 10 cm
(c) 12 cm
(d) 14 cm
Answer: (d)
Q21. (CBSE PYQ) If two tangents are drawn from an external point P, then PA and PB are
(a) Unequal
(b) Equal
(c) Parallel
(d) Perpendicular
Answer: (b)
Q22. Which statement is true?
(a) Radius is parallel to tangent
(b) Radius is perpendicular to tangent at point of contact
(c) Radius and tangent coincide
(d) Radius bisects tangent
Answer: (b)
Q23. The distance from the centre of a circle to a tangent is equal to
(a) Diameter
(b) Radius
(c) Chord
(d) Arc
Answer: (b)
Q24. A tangent to a circle cannot pass through the
(a) Point of contact
(b) Exterior point
(c) Centre
(d) Boundary of circle
Answer: (c)
Q25. If OP = 13 cm and radius = 5 cm, then tangent length PT is
(a) 10 cm
(b) 11 cm
(c) 12 cm
(d) 13 cm
Answer: (c) 12 cm
Solution: PT² = OP² − OT² = 13² − 5² = 144.
Q26. (CBSE PYQ) The tangent at any point of a circle is perpendicular to
(a) Chord
(b) Arc
(c) Diameter
(d) Radius through that point
Answer: (d)
Q27. If two tangents are drawn from point P, then triangle formed with centre O is
(a) Equilateral
(b) Isosceles
(c) Scalene
(d) Right only
Answer: (b)
Q28. A circle and tangent have exactly
(a) No common point
(b) One common point
(c) Two common points
(d) Three common points
Answer: (b)
Q29. If radius is doubled, diameter becomes
(a) Double
(b) Triple
(c) Four times
(d) Half
Answer: (a)
Q30. The angle between two radii of a circle is called
(a) Central Angle
(b) Tangent Angle
(c) Reflex Angle
(d) Exterior Angle
Answer: (a)
Q31. If a tangent touches the circle at A, then OA is
(a) Chord
(b) Radius
(c) Diameter
(d) Secant
Answer: (b)
Q32. If PA and PB are tangents and ∠APB = 60°, then triangle APB is
(a) Isosceles
(b) Equilateral
(c) Scalene
(d) Right
Answer: (a)
Q33. The shortest distance from centre to tangent is
(a) Radius
(b) Diameter
(c) Chord
(d) Arc
Answer: (a)
Q34. Which of the following touches the circle at one point?
(a) Diameter
(b) Chord
(c) Tangent
(d) Secant
Answer: (c)
Q35. If the radius of a circle is 10 cm, then the distance from centre to tangent is
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
Answer: (b)
Q36. (CBSE PYQ) If OP = 17 cm and radius = 8 cm, then tangent length from P is
(a) 15 cm
(b) 16 cm
(c) 17 cm
(d) 18 cm
Answer: (a)
Solution: √(17² − 8²) = √225 = 15 cm.
Q37. The theorem "Tangents from an external point are equal" applies to
(a) One tangent
(b) Two tangents
(c) Three tangents
(d) No tangent
Answer: (b)
Q38. Which line segment joins the centre to any point on the circle?
(a) Chord
(b) Diameter
(c) Radius
(d) Tangent
Answer: (c)
Q39. A secant intersects a circle at
(a) One point
(b) Two points
(c) Three points
(d) No points
Answer: (b)
Q40. If radius is 9 cm, diameter is
(a) 9 cm
(b) 18 cm
(c) 27 cm
(d) 36 cm
Answer: (b)
Q41. A tangent can be drawn at how many points on a circle?
(a) One
(b) Two
(c) Four
(d) Every point of the circle
Answer: (d)
Q42. (CBSE PYQ) If PA and PB are tangents from P, then PA − PB equals
(a) 1
(b) 0
(c) Radius
(d) Diameter
Answer: (b)
Q43. The point where a tangent touches the circle is called
(a) Centre
(b) Chord
(c) Point of Contact
(d) Radius
Answer: (c)
Q44. If OP = 25 cm and radius = 7 cm, tangent length is
(a) 24 cm
(b) 25 cm
(c) 26 cm
(d) 27 cm
Answer: (a)
Solution: √(25² − 7²) = √576 = 24 cm.
Q45. Which theorem is used in finding tangent length from an external point?
(a) BPT
(b) Pythagoras Theorem
(c) Midpoint Theorem
(d) Similarity Theorem
Answer: (b)
Q46. The radius drawn to the point of contact is always
(a) Parallel to tangent
(b) Equal to tangent
(c) Perpendicular to tangent
(d) Longer than tangent
Answer: (c)
Q47. If radius = 12 cm, then diameter =
(a) 12 cm
(b) 18 cm
(c) 20 cm
(d) 24 cm
Answer: (d)
Q48. The tangent segment joining external point to point of contact is
(a) Radius
(b) Diameter
(c) Tangent Length
(d) Arc
Answer: (c)
Q49. If two tangents are drawn from an external point, the angle between them depends on
(a) Radius only
(b) Circle only
(c) Position of external point
(d) Diameter only
Answer: (c)
Q50. Which statement is true?
(a) A tangent cuts the circle at two points.
(b) A radius through the point of contact is perpendicular to the tangent.
(c) Tangents from an external point are unequal.
(d) A circle has only two tangents.
Answer: (b) A radius through the point of contact is perpendicular to the tangent.
Solution: This is the fundamental theorem of tangents to a circle.