In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 10 Circles Ex 10.1. These solutions are based on new NCERT Syllabus.

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

Question 1.

How many tangents can a circle have?

Solution:

A circle can have an infinite number of tangents.

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) Exactly 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) \(\sqrt{119}\) cm

Solution:

In right ∆QPO,

OQ^{2} = OP^{2} + PQ^{2}

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:

We have the required figure, as shown

Here, l is the given line and a circle with centre O is drawn.

Line n is drawn which is parallel to l and tangent to the circle. Also, m is drawn parallel to line 1 and is a secant to the circle.

In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 10 Circles Ex 10.1. These solutions are based on new NCERT Syllabus.

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

Question 1.

How many tangents can a circle have?

Solution:

A circle can have an infinite number of tangents.

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) Exactly 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) \(\sqrt{119}\) cm

Solution:

In right ∆QPO,

OQ^{2} = OP^{2} + PQ^{2}

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:

We have the required figure, as shown

Here, l is the given line and a circle with centre O is drawn.

Line n is drawn which is parallel to l and tangent to the circle. Also, m is drawn parallel to line 1 and is a secant to the circle.