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) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
- 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.
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2.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.
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3.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.
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4.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is
- $\frac{5}{12}$
- $\frac{5}{6}$
- $1$
- $0$
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5.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is
- $50^\circ$
- $60^\circ$
- $45^\circ$
- $30^\circ$
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6.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
View Solution

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NCERT Solutions for Class 9 Maths Chapter 10: Circles

NCERT Solutions for Class 9 Mathematics Chapter 10