# NCERT Solutions For Class 10 Maths Chapter 10 Circles Ex 10.1

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 10 |

Exercise | Class 10 Maths Chapter 10 Circles Exercise 10.1 |

Number of Questions Solved | 4 |

## NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

**NCERT TEXTBOOK EXERCISES**

**Question 1. How many tangents can a circle have?**

**Solution:**

There can be infinitely many tangents to a circle.

**Question 2. Fill in the blanks:**

**(i)** A tangent to a circle intersects it in ………… point(s).**(ii)** A line intersecting a circle in two points is called a ………… .**(iii)** A circle can have parallel tangents at the most ………… .**(iv)** The common point of a tangent to a circle and the circle is called ……….. .

**Solution:**

**(i)** One**(ii)** Secant**(iii)** Two**(iv)** Point of contact.

**Question 3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is**

**(a)** 12 cm**(b)** 13 cm**(c)** 8.5 cm**(d)** √199 cm

**Solution:**

Radius of the circle = 5 cm

OQ = 12 cm

∠OPQ = 90°

[The tangent to a circle is perpendicular to the radius through the point of contact]

PQ^{2} = OQ^{2} – OP^{2} [By Pythagoras theorem]

PQ^{2} = 12^{2} – 5^{2} = 144 – 25 = 199

PQ = √199 cm.

Hence correct option is (d).

**Question 4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.**

**Solution:**

A line m is parallel to the line n and a line l which is secant is parallel to the given line.

## NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercise 10.1 PDF

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