NCERT Solutions for Exercise 10.1 Class 10 Maths Chapter 10 - Circles
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CBSE Class 10th Exam Date:01 Jan' 26 - 14 Feb' 26
The geometric definition of tangents to a circle provides the basic knowledge needed to study line interaction with curved shapes. The present exercise analyzes how tangents connect with circles at a single point while establishing their connection to radii together with chords and secants. The comprehension enables us to establish important properties through logical reasoning together with construction processes. Each question provides scenarios that require students to use triangle congruence and perpendicular lines together with the measured distance from a fixed point.
This Story also Contains
- NCERT Solutions Class 9 Maths Chapter 10: Exercise 10.1
- Topics covered in Chapter 10, Circles: Exercise 10.1
- NCERT Solutions of Class 10 Subject Wise
- NCERT Exemplar Solutions of Class 10 Subject Wise
Students benefit from the Exercise 10.1 NCERT Solutions from Class 10 Maths since these solutions help them effectively solve geometric problems. Core geometry abilities which form a foundation for advanced geometric methods become stronger through study of these fundamental characteristics in this field. The NCERT Books based exercise teaches students to identify the unique number of circle tangents together with the unique tangents from external points and their radius-tangent perpendicularity.
NCERT Solutions Class 9 Maths Chapter 10: Exercise 10.1
Q1 How many tangents can a circle have?
Answer:
Tangents are the lines that cross the circle precisely at a single point. There can be an endless number of tangents in a circle. This can be shown by the figures below:
Answer:
(a) One
In a single point, a circle's tangent crosses the circle precisely.
(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.
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) $\sqrt { 119}$ cm.
Answer:
It is given that the radius of the circle is 5 cm. OQ = 12 cm
According to the 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
Therefore, the correct option is (d) = $\sqrt { 119}$ cm
The supplied line is AB, and the line CD parallels the line AB and is the tangent to a circle at point M. A secant parallel to the AB is the line EF.
Also Read-
Topics covered in Chapter 10, Circles: Exercise 10.1
1. Concept and definition of a tangent to a circle: A straight line which touches a circle only at a single point without entering it makes up a tangent. At the point where a circle and the tangent line interact, there forms the point of contact while the tangent line remains at right angles to the radius drawn from this point.
2. Number of tangents a circle can have: A circle allows an infinite number of tangents to exist because one can create a tangent from every location on its circumference. A given point outside the circle permits only two possible tangents to touch it.
3. The condition of tangency (line touches the circle at only one point): A tangent maintains its extraordinary feature by never entering inside the circle while touching the circle exclusively at one point. Gas makes it unique from both secant and chord connections.
4. Use of Pythagoras' theorem in radius-tangent situations: A right triangle appears when drawing a tangent from outside the circle as the radius meets the line extending from the external point to the center. The tangent length becomes possible to calculate through the application of the Pythagoras theorem.
5. The length equality applies to tangents created when using any external point: Any two tangents originating from a common outside circle point share the identical length. The fundamental property proves useful throughout multiple geometric constructions along with multiple proofs.
6. Difference between secants and tangents: A secant connects two points on a circle and enters the interior while touching the circle only at one unique point. Identifying this distinction proves vital when resolving multiple geometric tasks related to circles.
Also see-
NCERT Solutions of Class 10 Subject Wise
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
NCERT Exemplar Solutions of Class 10 Subject Wise
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Frequently Asked Questions (FAQs)
Q: Explain the theorem covered in NCERT solutions for Class 10 Maths 10 exercise 10.1?
A:
The tangent is perpendicular to the radius via the point of contact at any point on a circle.
Q: How many activities are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1?
A:
Two activities are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1
Q: How are activities useful for NCERT solutions for Class 10 Maths 10 exercise 10.1?
A:
Ncert activities help us to visualize the concepts of tangent and circle by applying them in real life
Q: In the NCERT solutions for Class 10 Maths chapter 10 exercise 10.1, how many questions are covered?
A:
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.
Q: What are the requirements for solving NCERT solutions for Class 10 Maths chapter 10 exercise 10.1?
A:
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
Q: What is the tangent of a circle according to NCERT solutions for Class 10 Maths 10 exercise 10.1 ?
A:
A tangent is a line that intersects the circle at only one point
Q: How lines behave around a circle as specified in NCERT solutions for Class 10 Maths 10 exercise 10.1?
A:
Outside circle line does not touch any point, on circle line touches one point and in the circle, line touches two points
Q: How many theorems are covered till NCERT solutions for Class 10 Maths 10 exercise 10.1 ?
A:
Only one theorem is covered till NCERT solutions for Class 10 Maths 10 exercise 10.1
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The question papers will be available soon at the link attached herewith. You can keep an eye on the website of careers360. it will provide you perfect pattern of question papers, which will improve your writing skills and practice learning.
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You can download subject wise CBSE Sahodaya Class 10 Pre-Board Question Paper 2025-26 for Round 1 & Round 2 from this link : CBSE Sahodaya Class 10 Pre-Board Question Paper 2025-26
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Solving question papers is one of the best method of preparation. It gives you proper idea about the exam pattern and important topics to cover.
Here is the link attached from the official website of Careers360 which will provide you with the CBSE Sahodaya question papers. Hope it helps!
https://school.careers360.com/articles/sahodaya-question-paper-2025
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The CBSE Class 10 Hindi Question Paper Blueprint (Marking Pattern) for the 2025-2026 Board Exam is divided into four main sections, with a total of 80 marks for the written exam. The structure is slightly different for Hindi Course A and Hindi Course B.You can download the official Sample Question Paper (SQP) and its Marking Scheme for both Hindi Course A and Course B here: https://school.careers360.com/boards/cbse/cbse-class-10-hindi-sample-papers-2025-26
The CBSE Sahodaya Question Papers for Class 10 (2025-26) are not released centrally by the board as a single PDF.
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Local Release: The papers are designed and released by the individual Sahodaya School Clusters (groups of CBSE schools) just before or during the pre-board exam dates (typically held in December and January). Therefore, you must check your local cluster's portal or directly with your school administration.
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Best Practice: The official model papers, based on the full 2026 syllabus, are the most reliable tool for practice. These accurately reflect the structure, format, and competency-based questions used in the Sahodaya exams.
You can download the latest CBSE Class 10 Model Papers to simulate the Sahodaya tests here: https://school.careers360.com/articles/sahodaya-question-paper-2025 . Focus on that pattern
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