NCERT Solutions for Class 10 Maths Chapter 10: Circles

NCERT Solutions for Class 10 Maths Chapter 10 Circles deals with Circle and its various properties. In geometry, a circle is a perfectly round shape—meaning any point around its curve is the same distance from its central point. A circle consists of a closed curved line around a central point. Every point on the line is the same distance from the central point. This distance to the center is called the radius.

Class 10 Maths Chapter 10 Circles belongs to Unit 4 Geometry which has a weightage of 15 marks in the CBSE Class 10 Maths Examination. The questions related to tangent circle formula and semicircle are often asked in the Class 10 Examination.

Download PDF: NCERT Solutions for Class 10 Maths Chapter 10 Circles

NCERT Solutions for Class 10 Maths Chapter 10

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Important Topics in Class 10 Maths Chapter 10

A circle is a geometric figure that is measured in terms of its radius.

A circle and a line on a plane can have 3 possibilities – they can be non-intersecting they can have a single common point. they can have two common points.

Tangent: A tangent to a circle is a line that touches a circle at exactly one point.

For each point on a circle, there is a unique tangent that passes through it.

Secant: A secant is a line that has 2 common points with the circle.

Secant cuts the circle at exactly two points, forming a chord.

Tangent perpendicular to the radius at the point of contact.

The theorem states that “the tangent to a circle at any given point is the perpendicular to the radius of the circle which passes through the point of contact”

When a tangency point lies on a circle, exactly one tangent to a circle exists that passes through it.

The length of the tangents drawn from an external point to a circle are equal.

NCERT Solutions For Class 10 Maths Chapter 10 Exercises:

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

Circles – Related Topics:

Circles Revision Notes	Circles Important Questions	Cyclic Quadrilateral
Circle passing through 3 points	Perimeter and Area of a Circle	Circumference of Circle
Basic Proportionality Theorem	Area of Sector	Area of Segment of a Circle

CBSE Class 10 Mathematics Study Guides:

Geometry	Math Formula	Maths Study Material
NCERT Solutions for Class 10 Maths	Class 10 Maths Notes	Mensuration
Difference between in Maths	Calculus	Math MCQs

CBSE X Related Questions

1.
The natural number 1 is :
- a prime number.
- a composite number.
- prime as well as composite.
- neither prime nor composite.
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2.
In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.
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3.
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.
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4.
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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5.
The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is :
- 0
- 1
- 3
- 2
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6.
Prove that :
$\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$.
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