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NCERT Class 10 Maths Chapter 10 Online Test – Circles (50 MCQs) | Board Exam 2026

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NCERT Class 10 Maths Chapter 10 Online Test – Circles (50 MCQs) | Board Exam 2026
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NCERT Class 10 Mathematics – Chapter 10: Circles

Board Exam 2026 focused online test strictly based on NCERT textbook.

  • A tangent touches a circle at exactly one point.
  • The radius at the point of contact is perpendicular to the tangent.
  • Two tangents can be drawn from an external point.
  • Lengths of tangents from an external point are equal.
  • All results are proved using congruent triangles.

Q1. A tangent to a circle touches the circle at:

One point
Two points
No point
Infinite points
A tangent touches a circle at exactly one point.

Q2. The point where a tangent touches the circle is called:

Centre
Point of contact
Radius
Diameter
Definition as per NCERT.

Q3. The radius drawn to the point of contact is:

Parallel to tangent
Inclined to tangent
Perpendicular to tangent
Equal to tangent
Radius is perpendicular to tangent at point of contact.

Q4. A line intersecting a circle at two distinct points is called:

Radius
Tangent
Diameter
Secant
Definition of secant.

Q5. From an external point, the number of tangents to a circle is:

Two
One
Three
Infinite
Exactly two tangents are possible.

Q6. Tangents drawn from an external point are:

Unequal
Equal in length
Parallel
Perpendicular
NCERT theorem.

Q7. The common point of radius and tangent is:

Centre
Midpoint
Point of contact
Endpoint
Definition.

Q8. The tangent at any point of a circle is perpendicular to:

Diameter
Secant
Chord
Radius at that point
NCERT result.

Q9. From a point inside the circle, number of tangents possible:

Zero
One
Two
Infinite
No tangent from interior point.

Q10. From a point on the circle, number of tangents possible:

Two
One
Zero
Infinite
Exactly one tangent is possible.

Q11. The segment joining centre to point of contact is:

Chord
Diameter
Radius
Secant
Definition of radius.

Q12. A tangent does not pass through the:

Circumference
Point of contact
External point
Interior of the circle
Tangent never cuts interior.

Q13. The length of tangent from an external point is:

Finite
Infinite
Zero
Variable
Tangent segment has finite length.

Q14. If two tangents PA and PB are drawn from P, then:

PA > PB
PA = PB
PA < PB
PA + PB = radius
Lengths of tangents from external point are equal.

Q15. A chord passing through the centre is called:

Radius
Secant
Diameter
Tangent
Definition of diameter.

Q16. Tangent is always a:

Curve
Broken line
Ray
Straight line
Tangent is a straight line.

Q17. The centre of a circle lies:

Inside the circle
On circumference
Outside the circle
On tangent
Definition.

Q18. A secant always intersects the circle at:

One point
Two points
No point
Infinite points
Definition.

Q19. Tangent and radius meet at angle:

45°
60°
90°
180°
Perpendicular.

Q20. The tangent segment is measured between:

Two points on circle
Centre and contact
Two external points
External point and point of contact
Definition.

Q21. A tangent cannot be drawn from:

Interior point
External point
Point on circle
Two points
No tangent from interior point.

Q22. Radius is drawn from:

Circumference to circumference
Centre to circumference
Centre to centre
Circumference to tangent
Definition.

Q23. The length of radius is always:

Variable
Zero
Constant
Infinite
All radii of same circle are equal.

Q24. The diameter of a circle is:

Half the radius
Equal to radius
Twice the radius
Triple the radius
Diameter = 2 × radius.

Q25. Tangent touches the circle at:

One point
Two points
Three points
No point
Definition.

Q26. The angle between tangent and radius is:

45°
90°
60°
180°
Perpendicular.

Q27. A chord is:

Radius
Tangent
Line segment joining two points on circle
Diameter only
Definition of chord.

Q28. A diameter is the longest:

Radius
Tangent
Arc
Chord
Diameter is longest chord.

Q29. Tangents from same external point are:

Equal
Unequal
Parallel
Perpendicular
NCERT theorem.

Q30. The tangent at any point is perpendicular to:

Diameter
Radius at that point
Secant
Chord
Key property.

Q31. The centre of the circle lies on:

Tangent
Chord
Perpendicular to tangent
Secant
Centre lies on perpendicular to tangent.

Q32. Tangent is a special case of:

Chord
Diameter
Radius
Secant
Tangent is limiting case of secant.

Q33. Two tangents drawn from a point outside the circle meet at:

External point
Centre
Point of contact
Midpoint
Definition.

Q34. A circle has how many tangents?

Two
Infinite
One
Zero
Infinite tangents possible.

Q35. A tangent segment is part of:

Circle
Arc
Tangent
Radius
Definition.

Q36. The length of tangent depends on:

Radius only
Diameter only
Angle only
Distance of point from centre
Geometry.

Q37. A secant becomes a tangent when it:

Touches at one point
Cuts twice
Does not touch
Is curved
Limiting case.

Q38. The radius at point of contact makes angle with tangent:

60°
90°
30°
45°
Perpendicular.

Q39. All points on a circle are:

Unequal distance from centre
Inside
Equidistant from centre
Outside
Definition of circle.

Q40. The longest chord of a circle is:

Radius
Tangent
Arc
Diameter
Diameter is longest chord.

Q41. Tangent and radius form:

Right angle
Acute angle
Obtuse angle
Straight angle
Perpendicular.

Q42. A tangent does not intersect the circle at:

Point of contact
Two points
One point
External point
Only one point.

Q43. A chord through centre is:

Tangent
Radius
Diameter
Secant
Definition.

Q44. Tangent always touches circle:

Inside
Outside
Twice
At one point
Definition.

Q45. The radius is perpendicular to:

Tangent
Chord
Diameter
Secant
Key property.

Q46. A line touching a circle at one point is:

Chord
Tangent
Diameter
Secant
Definition.

Q47. Two tangents from external point meet at:

Centre
Circumference
External point
Midpoint
Definition.

Q48. Tangent is perpendicular to radius at:

Centre
Diameter
Any point
Point of contact
NCERT theorem.

Q49. A circle has how many points of contact with a tangent?

One
Two
Three
Infinite
Definition.

Q50. The chapter ‘Circles’ mainly deals with:

Area of circle
Tangents to a circle
Volume of sphere
Mensuration
NCERT scope.
Q1 Tangent touches at one point. Q2 Meaning of point of contact. Q3 Radius perpendicular to tangent. Q4 Definition of secant. Q5 Number of tangents from external point. Q6 Equality of tangents. Q7 Common point of radius and tangent. Q8 Tangent perpendicular to radius. Q9 Tangent from interior point. Q10 Tangent from point on circle. Q11 Radius definition. Q12 Tangent does not pass interior. Q13 Finite length of tangent. Q14 Equality of tangent segments. Q15 Definition of diameter. Q16 Tangent is straight line. Q17 Position of centre. Q18 Secant intersects twice. Q19 Angle between tangent and radius. Q20 Tangent segment definition. Q21 Tangent from interior impossible. Q22 Definition of radius. Q23 Equality of radii. Q24 Diameter relation. Q25 Tangent touches once. Q26 Angle between tangent and radius. Q27 Definition of chord. Q28 Diameter longest chord. Q29 Equal tangents. Q30 Tangent perpendicular to radius. Q31 Centre lies on perpendicular. Q32 Tangent is limiting case of secant. Q33 External point of tangents. Q34 Infinite tangents possible. Q35 Tangent segment. Q36 Dependence of tangent length. Q37 Secant becomes tangent. Q38 Perpendicular property. Q39 Definition of circle. Q40 Longest chord. Q41 Right angle formation. Q42 Single point of intersection. Q43 Chord through centre. Q44 Single point touch. Q45 Radius perpendicular. Q46 Definition of tangent. Q47 Meeting point of tangents. Q48 Point of contact. Q49 Single point of contact. Q50 Scope of circles chapter.
Disclaimer: We are not affiliated with NCERT. Although every care has been taken in creating this test, in case of any confusion, students should consider the NCERT textbooks and the opinion of their subject teacher as final.

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