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-

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  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.

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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.

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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.


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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.

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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:

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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

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

 

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

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

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 .

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

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.

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.

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

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

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