• School
  • Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 10 Notes - Download PDF

Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 10 Notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 19, 2022 12:51 PM IST

NCERT Class 10 Maths chapter 10 notes based on the circle, equation of circle graph of the circle, find radii of circle tangent and normal equation. The chapter circle Class 10 notes also includes how to draw a circle. CBSE Class 10 Maths chapter 10 notes include FAQ or frequently asked questions about the chapter. These topics can also be downloaded from Class 10 Maths chapter 10 notes pdf download.

This Story also Contains
  1. NCERT Class 10 Chapter 10 Notes-
  2. Circle in Two Variables Class 10 Notes- Topic 1:
  3. Definition of a Circle
  4. Equation of a Circle with Centre (h, k) and Radius-
  5. Equation of the Tangent:
  6. Equation of Normal:
  7. Equation of a Common Chord of the Two Circles-
  8. If two circles with centres C1 and C2 and radii r and r’ respectively, then we have the following results regarding their common tangents.
  9. Significance of NCERT Class 10 Maths Chapter 10 Notes
  10. Class 10 Chapter Wise Notes
  11. NCERT Solutions of Cass 10 Subject Wise
  12. NCERT Class 10 Exemplar Solutions for Other Subjects:

Also, students can refer,

NCERT Class 10 Chapter 10 Notes-

Circle in Two Variables Class 10 Notes- Topic 1:

Definition of a Circle

A circle is the locus of a point in a plane so that its distance from a fixed point in the plane is constant. The fixed point is called the centre of the circle and the constant distance is called the radius

Equation of a Circle with Centre (h, k) and Radius-

1644387517011

  1. Some results regarding circle

Position of a point with respect to a circle. Point P (x1, y1) lies outside, on, or inside a circle.

1644387515932

Here, r is the radius of the circle.

The point P is inside the circle when the distance is less than the radius. Then it is negative.

The point is outside the circle when the distance is greater than the radius. Then it is positive.

The point P is on the circle when distance and radius are equal. Then it is zero.

  1. Equation of the tangent to the circle from a point P (x1, y1)

Equation of the Tangent:

Equation of tangent to the circle x2+y2+2gx+2fy+c=0 from a point P (x1, y1)

xx1+yy1+g(x+x1)+f(y+y1)+c=0

It is the equation of the tangent.

  1. An equation of the Normal to the circle x2+y2+2gx+2fy+c=0 from a point P (x1, y1)

Equation of Normal:

x2+y2+2gx+2fy+c=0

(y-y1)/(y1+f)=(x-x1)/(x1+g)

It is the equation of normal.

Equation of a Common Chord of the Two Circles-

S1=x2+y2+2g1x+2f1y+c1=0

S2=x2+y2+2g2x+2f2y+c2=0

S1-S2=0

If two circles with centres C1 and C2 and radii r and r’ respectively, then we have the following results regarding their common tangents.

(x-h)2+(y-k)2=r2

(x-h')2+(y-k')2=r'2

Case 1. When C1 C2 > r+r’ i.e., the distance between the centers is greater than the sum of their radii, the two circles do not intersect with each other and 4 common tangents can be drawn to two circles.

Here C1and C2 are the centres of two circles.

In this case, two circles either touch each other externally or internally.

1644387516541

Case 2. When C1 C2 = r+r’ i.e., the distance between the centers is equal to the sum of the radii, the two circles touch each other externally, two direct common tangents are real and distinct and the transverse common tangents coincide.


1644387515605

Case 3. When C1 C2 < r+r’ i.e the distance between the centres is less than the sum of the radii, the circles intersect at two real and distinct points, the two direct common tangents are real and distinct while the transverse common tangents are imaginary.

1644387516235

Significance of NCERT Class 10 Maths Chapter 10 Notes

Circle Class 10 notes will be helpful to revise the chapter and to get an idea about the main topics covered in the chapter. CBSE Class 10 Maths chapter 10 notes also contain previous year’s questions and NCERT TextBook pdf. Circle Class 10 notes pdf download can be used to prepare in offline mode. Class 10 Maths chapter 10 notes contain frequently asked questions of the chapter.

Class 10 Chapter Wise Notes

NCERT Solutions of Cass 10 Subject Wise

NCERT Class 10 Exemplar Solutions for Other Subjects:

NCERT Books for Class 10
NCERT Syllabus for Class 10

Also Read

Articles

Upcoming School Exams

Bihar Open Board 10th Examination

Application Date:11 November,2024 - 10 January,2025

Bihar Open Board 12th Examination

Application Date:11 November,2024 - 10 January,2025

National Means Cum-Merit Scholarship

Admit Card Date:27 November,2024 - 22 December,2024

Gujarat Board Higher Secondary School Certificate

Late Fee Application Date:13 December,2024 - 22 December,2024

Madhya Pradesh State Open School 10th Examination

Admit Card Date:13 December,2024 - 31 December,2024

View All School Exams
Get answers from students and experts

Popular 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 More

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 More

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 More

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 More

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 More

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 More

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 More

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 More

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 More

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 More

Colleges After 12th

Popular Course After 12th

Applications for Admissions are open.

JEE Main Important Physics formulas
Apply

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

JEE Main Important Chemistry formulas
Apply

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

TOEFL ® Registrations 2024
Apply

Accepted by more than 11,000 universities in over 150 countries worldwide

Pearson | PTE
Apply

Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 31st DEC'24! Trusted by 3,500+ universities globally

JEE Main high scoring chapters and topics
Apply

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

JEE Main Important Mathematics Formulas
Apply

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

View All Application Forms
News and Notifications
Schools in Gurugram, Faridabad to hold classes in hybrid mode due to air pollution
CBSE files police complaint against two Delhi schools for submitting fake land certificates
Several Delhi schools receive bomb threat; fifth incident in nine days
Schools, colleges in Delhi NCR to switch to hybrid mode in view of air pollution
‘Take action’ on 22,298 unrecognised schools in UDISE Plus by March: Education ministry to states
Shiv Nadar School concludes 'Anandam 2024'; celebrating art, creativity in digital age
Jaipur: 10 students hospitalised after suspected gas leak at Mahesh Nagar coaching institute
Back to top