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.
In the given figure, \(TP\) and \(TQ\) are tangents to a circle with centre \(M\), touching another circle with centre \(N\) at \(A\) and \(B\) respectively. It is given that \(MQ = 13 \text{ cm}\), \(NB = 8 \text{ cm}\), \(BQ = 35 \text{ cm}\) and \(TP = 80 \text{ cm}\).
(i) Name the quadrilateral MQBN. (1)
(ii) Is MN parallel to PA? Justify your answer. (1)
(iii) Find length TB. (1)
(iv) Find length MN. (2)
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2.
If the median of the following distribution is 32.5, then find the values of x and y.
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3.
The natural number 2 is :
- a prime number
- a composite number
- prime as well as composite
- neither prime nor composite
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4.
In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 \text{ cm} \), \( BC = 3.5 \text{ cm} \) and \( HK = 7 \text{ cm} \), find the length of \( AC \).
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5.
Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).
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6.
The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :
- 0
- 1
- 3
- 2
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