NCERT Solutions For Class 10 mathematics Chapter 12:  Areas Related to Circles

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NCERT Solutions for Class 10 Mathematics chapter 12 Areas Related to Circles are provided in this article. Some of the important topics in Areas related to circle chapter include:

  1. Areas Related to Circles
  2. Perimeter and Area of a Circle
  3. Circumference of circle

Expected no of questions: 3 to 4 questions of total 6 to 7 marks

Download PDF: NCERT Solutions for Class Class 10 Mathematics Chapter 12 pdf


NCERT Solutions for Class 10 Mathematics Chapter 12

NCERT Solutions for Class 10 Mathematics Chapter 12 Areas Related to Circles is given below.

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Class 10 Mathematics Chapter 12 Areas Related to Circles – Important Topics

A circle is a simple geometrical figure surrounded by a curved line, which contains points separated by radius from a static point known as a centre. When a line and a circle are lying on the same plane and farther from each other, they do not intersect. But when the line comes in contact with the circle, it is tangent to the circle. That line intersects the two points of the curved line of the circle. The circle is a figure enclosed within a curved line which divides a plane into two regions: exterior and interior. A circle can also be understood as an ellipse where the two foci are concurrent and eccentricity is zero.

Circumference of circle: The perimeter of a circle is the distance covered by the boundary of a circle.

Segment of a circle: The segment is a region constrained by a chord of a circle and its arc.

Sector of a circle: A sector of a circle is clarified as the region of a circle enclosed by an arc and two radii.

Angle of a sector: The angle of the sector is the angle that is surrounded by the two radii of the sector.

Important formulas of this chapter include:

Length of Arc of a Sector L= (θ/360°)×2πr

Perimeter of a circle = 2πr

Area of a circle = πr2

NCERT Solutions for Class 10 Maths Chapter 12 Exercises

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Exercises is given below.

Chapter Related Articles:

Maths Related Articles:

CBSE X Related Questions

  • 1.
    Prove that : \(\sqrt{\frac{1 - \cos A}{1 + \cos A}} = \frac{\tan A}{\sec A + 1}\).


      • 2.
        There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:

        36(i) What is the total height of a mushroom ?


          • 3.
            In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions:

            37(i) Find \(m\angle AOP\).


              • 4.
                Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. Based on above information, answer the following questions:

                38(i) Represent the above situation in terms of a pair of linear equations in two variables.


                  • 5.
                    \(17 \times 11 \times 13 + 11\) is

                      • a prime number.
                      • multiple of 17.
                      • a composite number.
                      • an odd number.

                    • 6.
                      In the given figure, two triangles ABC and PQR are shown such that \(\angle A = \angle P\) and \(\angle C = \angle R\). If \(AD \perp BC\) and \(PS \perp QR\), then prove that (i) \(\Delta ADB \sim \Delta PSQ\) (ii) \(AD \times QS = BD \times PS\).

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