CBSE & NCERT Solutions for Class 10 Maths Circles Chapter 10
Introduction to the Circle
In this article, we will discuss Class 10 Maths Chapter 10 Circles. CBSE Class 10 student, you already have studied circle, arc, radius, sector, diameter, chord segment, etc.
Brief description: Circle is a collection of all the points in a plane surface which are at a constant distance from a center i.e. a fixed point.
Circumference is the outer parameter of the circle.
Radius can be a line from any point on the circumference to the center of the circle.
Now we will discuss a new topic as per CBSE Maths syllabus ‘Tangent to a circle’.
Tangent to a circle
In the above diagram, only one-point A is common to the circle and the line PQ, this is called Tangent to a circle. Therefore, as a definition, a line that intersects circle at one point only is called Tangent to the circle
Points to Ponder
- There is only one unique tangent at a point of the circle.
- When the two end points of its corresponding chord coincide thenthe tangent to a circle is a special case of the secant.
- The common point of the tangent and the circle is called the point of contact (Point A in above figure) and the tangent is said to touch the circle at the common point.
Now we will proceed ahead with theorem:
Theorem 1-The tangent from any point on a circle is perpendicular to the radius at the point of contact.
Given:-Circle with center O, Tangent XY to circle at point P
Required: – To Prove OP is perpendicular to XY.
Let’s take a point Q outside the circle on XY and join OQ.
As the point Q is outside the circle,OQ will be longer than the radius OP of the circle
If we will take any point on line XY, we will find that the above study will repeat for every point other than point P
OP is the shortest of all the distances, hence it perpendicular to XY.
Number of tangents from a point on a circle-
There can be 3 cases to find the number of tangents:
Case 1:-There is no tangent to a circle passing through a point lies inside the circle.
Case 2:-There is one and only one tangent to a circle passing through a point lying on the circle.
Case 3:-There can be exactly two tangents to a circle from a point which is outside the circle.
The length of a segment of the tangent from the external point P and the point of contact with the circle is called the length of the tangent.
We will discuss more theorems in the next article Class 10 Maths . Keep visiting the space for more.
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