Careers360 Logo
Search Colleges, Exams, Schools & more
ask-icon
share
    NCERT Solutions for Exercise 10.1 Class 10 Maths Chapter 10 - Circles

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

    #CBSE Class 10th
    Ramraj SainiUpdated on 30 Apr 2025, 03:24 PM IST

    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

    1. NCERT Solutions Class 9 Maths Chapter 10: Exercise 10.1
    2. Topics covered in Chapter 10, Circles: Exercise 10.1
    3. NCERT Solutions of Class 10 Subject Wise
    4. 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:
    1745464236191

    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
    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.

    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:

    It is given that the radius of the circle is 5 cm. OQ = 12 cm

    1745400919161

    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

    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:

    1745464158158

    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: ​​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 

    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.

    Articles
    Related Stories
    |
    Upcoming School Exams
    Manipur Board 12th Examination
    Ongoing Dates
    Manipur board 12th Admit Card Date

    17 Dec'25 - 20 Mar'26 (Online)

    Odisha Council of Higher Secondary Education 12th Examination
    Ongoing Dates
    Odisha CHSE Admit Card Date

    19 Dec'25 - 25 Mar'26 (Online)

    Kerala Department of Higher Secondary Education 12th Examination
    Ongoing Dates
    Kerala DHSE Admit Card Date

    15 Jan'26 - 28 Mar'26 (Online)

    Certifications By Top Providers
    Economic Evaluation for Health Technology Assessment
    Via Postgraduate Institute of Medical Education and Research Chandigarh
    Aspen Plus Simulation Software a Basic Course for Beginners
    Via Indian Institute of Technology Guwahati
    Yoga Practices 1
    Via Swami Vivekananda Yoga Anusandhana Samsthana, Bangalore
    Introduction to Biomedical Imaging
    Via The University of Queensland, Brisbane
    Brand Management
    Via Indian Institute of Management Bangalore
    Edx
     1071 courses
    Coursera
     816 courses
    Udemy
     394 courses
    Futurelearn
     264 courses
    Explore Top Universities Across Globe
    University of Essex, Colchester
    Wivenhoe Park Colchester CO4 3SQ
    University College London, London
    Gower Street, London, WC1E 6BT
    The University of Edinburgh, Edinburgh
    Old College, South Bridge, Edinburgh, Post Code EH8 9YL
    University of Nottingham, Nottingham
    University Park, Nottingham NG7 2RD
    Bristol Baptist College, Bristol
    The Promenade, Clifton Down, Bristol BS8 3NJ

    Questions related to CBSE Class 10th

    On Question asked by student community

    Have a question related to CBSE Class 10th ?
    cbse Class 8th syllabus for annual exam

    Dear Student,

    The Central Board of Secondary Education (CBSE) sets the syllabus of Class 8 subjects with the latest chapters and topics. The syllabus is the key to academic success.

    Download CBSE Class 8 Syllabus for 2025-26

    Read Complete Answer
    V
    Vivek Kumar
    13 Mar'26
    Cm shri school sample paper pdf for entrance
    Read Complete Answer
    V
    Vivek Kumar
    13 Mar'26
    I need CBSE class 10th Social science question paper 2025-26
    Read Complete Answer
    V
    Vivek Kumar
    13 Mar'26
    Can isee my result of my class 9

    Dear Student,

    Check your CBSE 9th Class Result 2026 Here

    Read Complete Answer
    V
    Vivek Kumar
    10 Mar'26
    CBSE class 10 exam centre Guwahati

    Hello Student,

    you can click on the article link. We have mentioned in detail on how to locate the centre.

    Link - CBSE Board Exam Centre List 2026: Class 10, 12 Center Locator/Finder

    Hope this helps!

    Read Complete Answer
    B
    Bhanu Pratap
    9 Mar'26
    View all

    Popular CBSE Class 10th Questions

    A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

    Option 1)

    0.34\; J

    		 Option 2)

    0.16\; J
    Option 3)

    1.00\; J

    		 Option 4)

    0.67\; J
    Read Complete Answer

    A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

    Option 1)

    2.45×10−3 kg

    		 Option 2)

     6.45×10−3 kg
    Option 3)

     9.89×10−3 kg

    		 Option 4)

    12.89×10−3 kg

     
    Read Complete Answer

    An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

    Option 1)

    2,000 \; J - 5,000\; J

    		 Option 2)

    200 \, \, J - 500 \, \, J
    Option 3)

    2\times 10^{5}J-3\times 10^{5}J

    		 Option 4)

    20,000 \, \, J - 50,000 \, \, J
    Read Complete Answer

    A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

    Option 1)

    K/2\,

    		 Option 2)

    \; K\;
    Option 3)

    zero\;

    		 Option 4)

    K/4
    Read Complete Answer

    In the reaction,

    2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

    Option 1)

    11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

    		 Option 2)

    6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
    Option 3)

    33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

    		 Option 4)

    67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
    Read Complete Answer

    How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

    Option 1)

    0.02

    		 Option 2)

    3.125 × 10-2
    Option 3)

    1.25 × 10-2

    		 Option 4)

    2.5 × 10-2
    Read Complete Answer

    If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

    Option 1)

    decrease twice

    		 Option 2)

    increase two fold
    Option 3)

    remain unchanged

    		 Option 4)

    be a function of the molecular mass of the substance.
    Read Complete Answer

    With increase of temperature, which of these changes?

    Option 1)

    Molality

    		 Option 2)

    Weight fraction of solute
    Option 3)

    Fraction of solute present in water

    		 Option 4)

    Mole fraction.
    Read Complete Answer

    Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

    Option 1)

    twice that in 60 g carbon

    		 Option 2)

    6.023 × 1022
    Option 3)

    half that in 8 g He

    		 Option 4)

    558.5 × 6.023 × 1023
    Read Complete Answer

    A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

    Option 1)

    less than 3

    		 Option 2)

    more than 3 but less than 6
    Option 3)

    more than 6 but less than 9

    		 Option 4)

    more than 9
    Read Complete Answer

    Applications for Admissions are open.

    JEE Main Important Physics formulas
    Get now

    As per latest syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

    JEE Main Important Chemistry formulas
    Get now

    As per latest syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

    JEE Main high scoring chapters and topics
    Get now

    As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

    JEE Main Important Mathematics Formulas
    Get now

    As per latest syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

    View all Application Forms

    CBSE Class 10th Notifications

    Latest updates

    Never miss CBSE Class 10th update

    Get timely CBSE Class 10th updates directly to your inbox. Stay informed!