Circles — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 10
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 10, "Circles". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Circles", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Circles, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Circles (Class 10 Mathematics)
A tangent touches a circle at exactly one point, and everything in this chapter follows from the fact that it is perpendicular to the radius at that point. From it come the equal-tangent property and the standard results about tangents from an external point.
- Tangent to a circle
- A line meeting the circle at exactly one point, called the point of contact. It never enters the interior of the circle.
- Secant
- A line cutting the circle at two distinct points. As the two points approach each other the secant becomes a tangent.
- Chord
- A segment joining two points on the circle; the longest chord is the diameter, which passes through the centre.
- Tangent perpendicular to radius
- The tangent at any point is perpendicular to the radius drawn to that point — the theorem the whole chapter rests on.
Circles — important questions & MCQs with answers (Class 10 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Number of tangents from an external point to a circle:
A.1B.0C.2✓ CorrectD.InfiniteAnswer: C. 2
Explanation: An external point lies outside the circle, so exactly two distinct tangent lines can be drawn to it — a point inside allows none, a point on the circle allows only one.
- Q2Easy
Tangent at any point of a circle is ___ to the radius at the point of contact.
A.ParallelB.Perpendicular✓ CorrectC.EqualD.IntersectingAnswer: B. Perpendicular
Explanation: The tangent-radius theorem: a tangent touches the circle at exactly one point, and at that point it is always perpendicular (⟂) to the radius — never parallel or merely equal in length.
- Q3Easy
A tangent to a circle:
A.Touches the circle at exactly one point✓ CorrectB.Cuts the circle at two pointsC.Passes through the centreD.Does not intersect the circleAnswer: A. Touches the circle at exactly one point
Explanation: By definition, a tangent touches a circle at exactly one point without crossing into the interior — unlike a secant, which cuts through at two points, or a line through the centre.
- Q4Easy
The longest chord of a circle is the:
A.SecantB.RadiusC.TangentD.Diameter✓ CorrectAnswer: D. Diameter
Explanation: A chord's length is 2√(r² − d²), where d is its distance from the centre; this is largest when d = 0, i.e. when the chord passes through the centre — that chord is the diameter.
- Q5Easy
The number of tangents that can be drawn to a circle from a point outside it is:
A.1B.0C.infinitely manyD.2✓ CorrectAnswer: D. 2
Explanation: From an external point exactly two tangents can be drawn to a circle, and they are equal in length.
- Q6Easy
The distance between two parallel tangents of a circle of radius 7 cm is:
A.28 cmB.7 cmC.14 cm✓ CorrectD.22 cmAnswer: C. 14 cm
Explanation: Parallel tangents touch the ends of a diameter, so they are 2 × 7 = 14 cm apart.
- Q7Medium
Radius=5, distance from external point P to centre=13. Tangent length from P:
A.8B.12✓ CorrectC.18D.7Answer: B. 12
Explanation: The tangent is perpendicular to the radius, so tangent = √(OP² − r²) = √(13² − 5²) = √144 = 12.
- Q8Medium
Tangents from an external point to a circle are:
A.UnequalB.Always 5 cmC.Perpendicular to each otherD.Equal in length✓ CorrectAnswer: D. Equal in length
Explanation: Since OA = OB (radii) and OP is common, right triangles OAP and OBP (right-angled at A, B where tangent ⟂ radius) are congruent, so tangents PA and PB from P are equal in length.
- Q9Medium
In a quadrilateral ABCD circumscribing a circle, AB + CD equals:
A.AB onlyB.AC + BDC.BC + AD✓ CorrectD.2(BC + AD)Answer: C. BC + AD
Explanation: Tangent lengths from each vertex are equal, so every tangent segment is counted once on each side; summing opposite sides gives AB + CD = BC + AD — the Pitot theorem for tangential quadrilaterals.
- Q10Medium
A chord of length 24 cm lies 5 cm from the centre of a circle. The radius of the circle is:
A.12 cmB.13 cm✓ CorrectC.17 cmD.10 cmAnswer: B. 13 cm
Explanation: Half the chord is 12 cm, so the radius is √(144 + 25) = 13 cm.
- Q11Medium
PA and PB are tangents from an external point P to a circle with centre O. If ∠APB = 80°, then ∠POA is:
A.50°✓ CorrectB.100°C.40°D.80°Answer: A. 50°
Explanation: ∠AOB = 180° − 80° = 100°, and OP bisects it, so ∠POA = 50°.
- Q12Hard
PA and PB are tangents from P to a circle of radius 3 cm with centre O, and OP = 5 cm. The area of quadrilateral OAPB is:
A.6 cm²B.24 cm²C.12 cm²✓ CorrectD.15 cm²Answer: C. 12 cm²
Explanation: Each tangent is √(25 − 9) = 4 cm, and the figure is two right triangles of area 6 cm² each.
- Q13Hard
Two tangents from external point P make 60°. Angle subtended by them at centre:
A.120°✓ CorrectB.60°C.90°D.30°Answer: A. 120°
Explanation: Tangent ⟂ radius gives right angles at both points of contact, so in the kite formed by the tangents and radii, the centre angle and the 60° angle at P sum to 180°: centre angle = 180° − 60° = 120°.
- Q14Hard
PA and PB are tangents to a circle with centre O. If ∠APB = 50°, then ∠OAB equals:
A.65°B.25°✓ CorrectC.50°D.115°Answer: B. 25°
Explanation: Tangent ⟂ radius gives right angles at the contact points, so ∠AOB = 180° − ∠APB = 130°; triangle OAB is isosceles (OA = OB = r), giving ∠OAB = (180° − 130°)/2 = 25°.
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Start this chapter free →Circles — FAQs
What are the key concepts in Class 10 Mathematics Circles?+
A tangent touches a circle at exactly one point, and everything in this chapter follows from the fact that it is perpendicular to the radius at that point. From it come the equal-tangent property and the standard results about tangents from an external point. Key ideas include Tangent to a circle, Secant, Chord, Tangent perpendicular to radius.
What does Class 10 Mathematics Chapter 10 (Circles) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Circles": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Circles" questions free to practise?+
Yes. Sign in with Google to practise "Circles" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Circles" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Circles" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Circles" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Circles (Class 10 Mathematics)?+
The questions that matter most test Tangent to a circle, Secant, Chord, Tangent perpendicular to radius. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Circles?+
Yes — Class 10 Mathematics Circles has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.