Class 10 Mathematics Chapter 10: Circles — practice questions with answers
Free practice for Class 10 Mathematics, Chapter 10: Circles. Try the solved questions below, then take a free test with instant marking and explanations.
54 questions24 easy, 20 medium, 10 hardNCERT · CBSE · State boards
Sample questions with solutions
Q1. A line that meets a circle in exactly one point is called a ______.
- tangent
- secant
- chord
- diameter
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Answer: A. tangent
Why: The common point is the point of contact. [p.144]
Why: The common point is the point of contact. [p.144]
Q2. A line that intersects a circle in two points is called a ______.
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Answer: secant
Why: Fig. 10.1(ii): the line meets the circle at A and B. [p.144]
Why: Fig. 10.1(ii): the line meets the circle at A and B. [p.144]
Q3. The common point of a tangent and a circle is called the point of ______.
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Answer: contact
Why: The tangent touches the circle at the point of contact. [p.146]
Why: The tangent touches the circle at the point of contact. [p.146]
Q4. Theorem 10.1 states that the tangent at any point of a circle is ______ to the radius through the point of contact.
- perpendicular
- parallel
- equal
- inclined at 45°
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Answer: A. perpendicular
Why: OP ⊥ XY because OP is the shortest distance from O to the tangent. [p.146]
Why: OP ⊥ XY because OP is the shortest distance from O to the tangent. [p.146]
Q5. Theorem 10.2 states that the lengths of the tangents drawn from an external point to a circle are ______.
- equal
- unequal
- in ratio 1 : 2
- equal to the radius
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Answer: A. equal
Why: PQ = PR by RHS congruence. [p.149]
Why: PQ = PR by RHS congruence. [p.149]
Q6. The line containing the radius through the point of contact is sometimes called the normal to the circle at that point.
True or false?
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Answer: True
Why: Remark 2 after Theorem 10.1. [p.147]
Why: Remark 2 after Theorem 10.1. [p.147]
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Frequently asked questions
How many practice questions are there for Class 10 Mathematics Chapter 10: Circles?
54 questions (24 easy, 20 medium, 10 hard). A few are solved on this page; the free test shows the answer and explanation for every question after you submit.
Is this chapter from the NCERT book?
Yes — it follows the NCERT Class 10 Mathematics syllabus, used by CBSE and many state boards.