## CBSE & NCERT Solutions for Class 10 Maths Circles Chapter 10

__Introduction to the Circle__

__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

OQ>OP.

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.

One stop solution for CBSE** NCERT Solutions** and **Best Online Classes** for *Class 10*, kindly visit takshilalearning.

**Follow Us on Social media : **

## 0 responses on "CBSE & NCERT Solutions for Class 10 Maths Circles Chapter 10"