Class 10 Maths NCERT Solutions Chapter 10 Circles - Exercise 10.1

Class 10 Maths NCERT Solutions Exercise 10.1: Mathematics is one of the most important subjects included in the CBSE Class 10 curriculum. Securing good marks in this subject is crucial for achieving academic success. Among the various chapters in Class 10 Mathematics, Circles hold a significant position, as it is one of the highest-weighing chapters and is also crucial for understanding various concepts and applications of geometry. Therefore students must focus on circles to understand the fundamentals and practise several questions to master the concepts.

NCERT Solutions for Class 10 Circles serve as an invaluable resource for students preparing for the board exams. This article includes NCERT Solutions for Class 10 Math Circles Exercise 10.1. These solutions provide step-by-step explanations and detailed reasoning for each question in the exercise. Following these NCERT solutions by subject experts will enable students grasp the underlying concepts thoroughly. By practising these solutions, students can develop a strong foundation in concepts related to circles and enhance their problem-solving skills. This would ultimately help them ace their board exams.

Highlights of NCERT Solutions for Class 10 Maths Exercise 10.1

Check solutions to all questions below:

NCERT Solutions for Class 10 Maths Circles - Exercise 10.1

Question 1: How many tangents can a circle have?

Solution: A circle can have infinite 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)A tangent to a circle intersects it in one point (s).

(ii)A line intersecting a circle in two points is called a secant.

(iii)A circle can have two parallel tangents at the most.

(iv)The common point of a tangent to a circle and the circle is called 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) √119 cm

Solution: We know that the line drawn from the centre of the circle to the tangent is perpendicular to

the tangent.

OP ⊥PQ

By applying Pythagoras theorem in ΔOPQ,

OP² + PQ² = OQ2

5² + PQ² = 122

PQ² = 144 − 25

PQ = √119 cm.

Hence, the correct answer 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:

AB ∥CD

Line AB is intersecting the circle at exactly two points, P and Q.

Therefore, line AB is the secant of this circle.

Since line CD is intersecting the circle at exactly one point, R, line CD is the tangent to the circle.

You can also check NCERT Solutions for all exercises of Chapter 10 - Circles from the link given below. All solutions can be downloaded in PDF format.