NCERT Solutions for Class 9 Maths Chapter 10: Circles

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The NCERT Solutions for class 9 Maths Chapter 10 Circles have been provided in the article below. A circle is the collection of all the points in a plane where, each of which is at a constant distance from a fixed point in that particular plane. A circle refers to the path of a point which moves in a plane in such a way that it remains at a constant distance from a fixed point in a plane.

Class 9 Maths Chapter 10 Circles belong to Unit 4 Geometry which has a weightage of 27 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 10 cover the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 10 pdf

NCERT Solutions for Class 9 Mathematics Chapter 10

Important Topics in Class 9 Maths Chapter 10 Circles

Important Topics in Class 9 Maths Chapter 10 Circles are given below:

Cyclic Quadrilateral

Cyclic quadrilaterals are a type of quadrilaterals that have four vertices lying on the circumference of the same circle. It is simply a quadrilateral circumscribed within a circle.

Example: State the Brahmagupta Theorem.

Solution: Brahmagupta theorem helps determine the area and perimeter of a cyclic quadrilateral.
Area, ‘K’, of a cyclic quadrilateral that has sides a, b, c, and d can be expressed by:
K = \(\sqrt{( s − a ) ( s − b ) ( s − c ) ( s − d) } \)
Now, the perimeter of the respective quadrilateral can be expressed as 2S. Thus, S is the semi perimeter which can be showed as,
S = (1/2) × (a + b + c + d)

Semi Circle

Geometrically, a semicircle is a plane two-dimensional shape which can be formed by dividing a circle into exactly two segments.

Example: What is the area and perimeter of a semicircle?

Solution: The Area of a semicircle is = 1/2 (π r²)
The Perimeter of a semicircle is = (1/2) πd + d

Tangent to a Circle

A tangent to a circle is a line that touches the curved line or surface at a single point in geometry. A tangent to a circle can be expressed as a line that intersects the circle at a single point.

Example: List three properties of a Tangent.

Solution: The properties of a Tangent are:

The tangent is known to make a single point contact with the respective circle.
When the tangency occurs, it remains perpendicular to the circle's radius.
The tangent can never have two points intersecting the circle.

NCERT Solutions for Class 9 Maths Chapter 10 Exercises:

The detailed solutions for all the NCERT Solutions for Circles under different exercises are:

Also Read:

Unit Related Topics
Tangent Circle Formula	Class 9 Maths Chapter 10 Circles MCQs	Circles Revision Notes
Circumference of a Circle	Central Angle of a Circle	Great Circle Formula

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CBSE X Related Questions

1.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
2.
The graph of a quadratic polynomial f(x) passes through (5,0), (0, -1) and (-2, 0). The two factors of the polynomial are
- \((x + 2), (x - 5)\)
- \((x + 5), (x - 2)\)
- \((x + 1), (x - 5)\)
- \((x - 1), (x + 2)\)
View Solution
3.
Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is
- \(10^{\circ}\)
- \(60^{\circ}\)
- \(45^{\circ}\)
- \(100^{\circ}\)
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4.
If \(PQ\) and \(PR\) are tangents to the circle with centre \(O\) and radius \(4 \text{ cm}\) such that \(\angle QPR = 90^{\circ}\), then the length \(OP\) is
- \(4 \text{ cm}\)
- \(4\sqrt{2} \text{ cm}\)
- \(8 \text{ cm}\)
- \(2\sqrt{2} \text{ cm}\)
View Solution
5.
There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?
- 144
- 2
- 420
- 272
View Solution
6.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is
- \(0\)
- \(\frac{80}{81}\)
- \(1\)
- \(\frac{82}{80}\)
View Solution

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NCERT Solutions for Class 9 Maths Chapter 10: Circles

NCERT Solutions for Class 9 Mathematics Chapter 10