# Circles Class 10 Notes: Chapter 10

**CBSE Class 10 Maths Circles Notes:-**Download PDF Here

A brief introduction to circles for class 10 is provided here. Get the complete description provided here to learn about the concept of the circle. Also, learn how to draw a tangent to the circle with various theorems and examples.

## Introduction to Circles

#### For More Information On Circles, Watch The Below Videos.

To know more about Circles, visit here.

### 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.

### Tangent

A **tangent to a circle **is a line that touches the circle at exactly one point. For every point on the circle, there is a unique tangent passing through it.

To know more about Tangent, visit here.

### Secant

A **secant to a circle** is a line that has two points in common with the circle. It cuts the circle at two points, forming a chord of the circle.

To know more about Secant, visit here.

### Tangent as a special case of Secant

** **The tangent to a circle can be seen as a special case of the secant when the two endpoints of its corresponding chord coincide.

### Two parallel tangents at most for a given secant

For every given **secant** of a circle, there are **exactly two tangents which are parallel** to it and touches the circle at two **diametrically opposite points.**

## Theorems

### Tangent perpendicular to the radius at the point of contact

**Theorem**: The theorem states that “the **tangent **to the circle at any point is the **perpendicular to the radius** of the circle that passes through the point of contact”.

Here, O is the centre and OP⊥XY.

#### For More Information On Perpendicular Tangent Theorem, Watch The Below Video.

### The number of tangents drawn from a given point

i) If the point is in an **interior region of the circle**, any line through that point will be a secant. So, **no ****tangent **can be drawn to a circle which passes through a point that lies inside it.

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 length of the tangent from the point (Say P) to the circle is defined as the segment of the tangent from the external point **P** to the point of tangency **I** with the circle. In this case, PI is the tangent length.

### Lengths of tangents drawn from an external point

**Theorem: **Two tangents are of equal length when the tangent is drawn from an external point to a circle.

PT1=PT2

Thus, the two important theorems in Class 10 Maths Chapter 10 Circles are:

**Theorem 10.1:** The tangent at any point of a circle is perpendicular to the radius through the point of contact.

**Theorem 10.2: **The lengths of tangents drawn from an external point to a circle are equal.

**Interesting facts about Circles and its properties are listed below:**

- In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
- The tangents drawn at the ends of a diameter of a circle are parallel.
- The perpendicular at the point of contact to the tangent to a circle passes through the centre.
- The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
- The parallelogram circumscribing a circle is a rhombus.
- The opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

To know more about Tangent Circle, visit here.