NCERT Mathematics · Class 10 · English · 2026-27

Circles — Exercise 10.1

Independently written, step-by-step solutions. Prompts below are concise paraphrases; use the official textbook for the complete question wording.

Choose a question

Question 1

How many tangents does a circle have?

Step-by-step solution

Every point of the circumference has one tangent, and a circle has infinitely many points.

Answer: Infinitely many.

Resource ID: CB-10-M-CH10-EX10.1-Q1

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Question 2

Complete the four statements about tangents and secants.

Step-by-step solution

A tangent meets a circle at exactly one point, while a secant meets it at two distinct points. For a fixed direction, parallel tangents lie on the two opposite sides of the circle.

Answer: (i) One; (ii) secant; (iii) two; (iv) point of contact (point of tangency).

Resource ID: CB-10-M-CH10-EX10.1-Q2

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Question 3

A tangent PQ touches at P, with OP=5 cm and OQ=12 cm. Find PQ.

Step-by-step solution

The radius OP is perpendicular to PQ, so OQ is the hypotenuse. PQ²=OQ²−OP²=144−25=119.

Answer: PQ=√119 cm, choice D.

Resource ID: CB-10-M-CH10-EX10.1-Q3

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Question 4

Draw a circle with a tangent and a secant parallel to a given line.

Step-by-step solution

Draw a radius perpendicular to the given line. Through its endpoint draw a parallel line: it is perpendicular to that radius, hence tangent. Through the centre draw another parallel; it cuts the circle twice, hence is a secant.

Parallel tangent and secant constructionTangentSecantGiven directionO
Answer: The construction below meets both conditions.

Resource ID: CB-10-M-CH10-EX10.1-Q4

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