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The distance from any point on the circle to the fixed point is the radius.
Which chapter is very difficult in maths?
The toughest chapter in Class 10 Maths varies among students, but topics like Quadratic Equations, Triangles, and Surface Areas and Volumes are often perceived as challenging due to their abstract concepts and complex calculations.
Who invented circle?
The first theorems relating to circles are attributed to Thales around 650 BC.
CBSE Class 10 Maths Notes Chapter 10 Circles
Here, we have provided CBSE Class 10 Maths Notes Chapter 10. Students can view these CBSE Class 10 Maths Notes Chapter 10 Circles before exams for better understanding of the chapter.
Neha Tanna22 Apr, 2024
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CBSE Class 10 Maths Notes Chapter 10:
Here is a quick overview of circles for students in Class 10. Learn about the notion of the circle by reading the full explanation given here. Discover how to draw a tangent to the circle using a variety of examples and theorems.
Concepts including an introduction to circles, tangents to circles, and the number of tangents from a point on a circle are covered in Class 10 Maths Chapter 10, "Circles."
CBSE Class 10 Maths Notes Chapter 10 PDF
Students can get free CBSE Solutions (NCERT) and other study materials from the website. To help you review the entire syllabus and get better grades in your exams, you can download the Class 10 Maths NCERT Solutions.
As is common knowledge, a circle is a closed, two-dimensional geometric object in which every point on its surface is equally spaced from the point known as its "centre." "Radius" is the measurement of the separation between a circle's centre and any point on its surface.
Circle and Line in a Plane
For a circle and a line on a plane, there can be
three
possibilities.
i) they can be
non-intersecting
ii) they can have
a single common point:
in this case, the line touches the circle.
ii) they can have
two common points:
in this case, the line cuts the circle.
(i) Non-intersecting (ii) Touching (iii) Intersecting
A line that shares two points with a circle is called a secant to the circle. It creates a chord of the circle by cutting it at two spots.
Tangent as a Special Case of Secant
When the two ends of the corresponding chord of a tangent to a circle coincide, the tangent can be thought of as a specific case of the secant.
Two Parallel Tangents at most for a Given Secant
There are precisely two tangents that are parallel to a circle and touch it at two diametrically opposed locations for each secant of a circle.
From the given diagram, we can observe the following points:
PQ is the secant of a circle.
P’Q’ & P”Q” are two tangents which are parallel to PQ.
Theorems
Tangent Perpendicular to the Radius at the Point of Contact
"The tangent to the circle at any point is the perpendicular to the radius of the circle that passes through the point of contact," according to the theorem.
Here, O is the centre and
O
P
⊥
X
Y
.
Theorem Proof:
Let us consider a circle with centre "O" and tangent XY at point "P." We must now demonstrate that OP is perpendicular to the XY tangent.
Now imagine a point Q different than P on the tangent line XY. As seen in the figure, join the OQ points.
Point Q should be outside the circle in this instance. For XY will not be a tangent to the circle if the point Q is inside the circle. It implies that XY will join a circle as a secant.
So, OQ should be greater than the radius of the circle OP.
It means that
OQ > OP
Since all points on line XY, except P, comply with this requirement, the shortest distance between the centre of the circle "O" and the points on line XY should be found at OP.
As a result, we can say that OP is not parallel to XY.
The theorem is so demonstrated.
The Number of Tangents Drawn from a Given Point
i) Any line passing through the point will be a secant if it is located inside the circle. Therefore, if a circle passes through a point that is inside it, no tangent can be traced to it.
AB is a secant drawn through the point S
ii) When a point of tangency lies on the circle, there is
exactly one tangent
to a circle that passes through it.
iii) When the point lies outside of the circle, there are
accurately two tangents
to a circle through it
Length of a Tangent
The segment of the tangent from the external point P to the point of tangency I with the circle is the length of the tangent from the point (say P) to the circle. The tangent length in this instance is PI.
Benefits of CBSE Class 10 Maths Notes Chapter 10
Provide concise, understandable descriptions of important ideas.
Simplifies difficult subjects for easier comprehension.
Effective study aid for final exam preparation.
Improves the recall of important information.
Offers essential points and advice to help with efficient exam preparation.
Combines information to save time.
Gives priority to significant subjects and inquiries.
Provides useful illustrations for linkages to the actual world.
Increases students' exam-taking confidence.
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From the given diagram, we can observe the following points:
