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NCERT Solutions for Exercise 10.1 Class 10 Maths Chapter 10 - Circles

NCERT Solutions for Exercise 10.1 Class 10 Maths Chapter 10 - Circles

Edited By Ramraj Saini | Updated on Nov 27, 2023 01:39 PM IST | #CBSE Class 10th

NCERT Solutions For Class 10 Maths Chapter 10 Exercise 10.1

NCERT Solutions for Exercise 10.1 Class 10 Maths Chapter 10 Circles are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 maths ex 10.1introduces us to a circle. The circle is very widely used in whole mathematics introducing basic terminologies related to circle.

This Story also Contains
  1. NCERT Solutions For Class 10 Maths Chapter 10 Exercise 10.1
  2. Circles Class 10 Chapter 10 Circles Exercise: 10.1
  3. More About NCERT Solutions for Class 10 Maths Exercise 10.1
  4. Benefits of NCERT Solutions for Class 10 Maths Exercise 10.1
  5. NCERT Solutions Subject Wise
  6. Subject Wise NCERT Exemplar Solutions

NCERT solutions for exercise 10.1 Class 10 Maths chapter 10 Circles focus is on information about tangent such as what tangent is, its relationship with circle along with this we are introduced with the first theorem of chapter circle. 10th class Maths exercise 10.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

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Circles Class 10 Chapter 10 Circles Exercise: 10.1

Q1 How many tangents can a circle have?

Answer:

The lines that intersect the circle exactly at one single point are called tangents. In a circle, there can be infinitely many tangents.

15942926237221594292621263

Q2 Fill in the blanks :
(1) A tangent to a circle intersects it in_________ point (s).
(2) A line intersecting a circle in two points is called a _____.
(3) A circle can have ________ parallel tangents at the most.
(4) The common point of a tangent to a circle and the circle ______

Answer:

(a) one
A tangent of a circle intersects the circle exactly in one single point.

(b) secant
It is a line that intersects the circle at two points.

(c) Two,
There can be only two parallel tangents to a circle.

(d) point of contact
The common point of a tangent and a circle.

Q3 A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center 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.

Answer:

The correct option is (d) = \sqrt { 119} cm

15942929967351594292993758
It is given that the radius of the circle is 5 cm. OQ = 12 cm
According to question,
We know that \angle QPO=90^0
So, triangle OPQ is a right-angle triangle. By using Pythagoras theorem,
PQ =\sqrt{OQ^2-OP^2}=\sqrt{144-25}
=\sqrt{119} cm

Q4 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.

Answer:

15942930944311594293092133
AB is the given line and the line CD is the tangent to a circle at point M and parallels to the line AB. The line EF is a secant parallel to the AB

More About NCERT Solutions for Class 10 Maths Exercise 10.1

Class 10 Maths chapter 10 exercise 10.1 is a very short exercise. It is like a base exercise about the whole chapter circle and further concepts of the circle in higher classes. The questions in exercise 10.1 Class 10 Maths, broadly consist of four types of questions. Firstly we have a very basic question about circles and tangents then we have to fill in the blank questions about the properties of circles. NCERT solutions for Class 10 Maths exercise 10.1 also consist of questions in which we have to find the length of the circle along with this we have a construction based question in which have to construct the given situation about circles, tangents and straight lines. The basic knowledge about straight lines is also required to understand the NCERT solutions for Class 10 Maths exercise 10.1. Exercise 10.1 Class 10 Maths covers all types of basic and theory questions that can be formed on the circle and tangents.

Also Read| Circles Class 10th Notes

Benefits of NCERT Solutions for Class 10 Maths Exercise 10.1

  • Class 10 Maths chapter 10 exercise 10.1 broadly covers a basic knowledge about circles and tangents which we would be required to proceed in Class 10 Maths chapter 10 exercise 10.2
  • Exercise 10.1 from NCERT Class 10 Maths chapter 10 will be useful in Class 11 Maths chapter 11 conic sections.
  • As NCERT Class 10 Maths chapter 10 exercise 10.1 is a building block for question so it is a very important chapter for class 11, competitive exams and Olympiads

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NCERT Solutions Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Question (FAQs)

1. ​​What are the requirements for solving NCERT solutions for Class 10 Maths chapter 10 exercise 10.1?

Concepts covered in Class 9 such as radius, centre, chord, segment and sector are prerequisite for NCERT solutions for Class 10 Maths chapter 10 exercise 10.1 

2. What is the tangent of a circle according to NCERT solutions for Class 10 Maths 10 exercise 10.1 ?

A tangent is a line that intersects the circle at only one point

3. How lines behave around a circle as specified in NCERT solutions for Class 10 Maths 10 exercise 10.1?

Outside circle line does not touch any point, on circle line touches one point and  in the circle, line touches two points

4. How many theorems are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1 ?

Only one theorem is covered till NCERT solutions for Class 10 Maths 10 exercise 10.1 

5. Explain the theorem covered in NCERT solutions for Class 10 Maths 10 exercise 10.1?

The tangent is perpendicular to the radius via the point of contact at any point on a circle.

6. How many activities are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1?

Two activities are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1

7. How are activities useful for NCERT solutions for Class 10 Maths 10 exercise 10.1?

Ncert activities help us to visualize the concepts of tangent and circle by applying them in real life 

8. In the NCERT solutions for Class 10 Maths chapter 10 exercise 10.1, how many questions are covered?

There are 4 questions in Class 10 Maths chapter exercise 10.1. Question 2 consists of four fill in the blank  Question 3 consists of 4 subparts.

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