Feedback

What do you think about us?

Your name

Your email

Message

Understanding tangents to a circle involves recognizing their unique properties, such as touching the circle at only one point and being perpendicular to the radius at the point of tangency. This text explains how to calculate the gradient of the radius and the tangent line, and how to formulate the tangent's equation using the point-slope formula. A worked example demonstrates the application of these concepts to find the equation of a tangent line at a specific point on a circle.

Show More

## Definition of a Tangent

### Point of Tangency

A point where a tangent line touches a circle at exactly one point

### Perpendicular Relationship

Radius and Tangent

The tangent line is always perpendicular to the radius of the circle at the point of tangency

### Distinction from a Secant

A tangent only intersects a circle at one point, while a secant intersects at two points

## Finding the Equation of a Tangent Line

### Determining the Gradient of the Radius

The gradient of the radius is calculated using the coordinates of the circle's center and the point of tangency

### Calculating the Gradient of the Tangent

The gradient of the tangent is the negative reciprocal of the gradient of the radius

### Formulating the Equation of the Tangent Line

The equation of the tangent line can be found using the point-slope form with the gradient of the tangent and the point of tangency

## Example Problems

### Tangent to a Circle with a Given Point

To find the equation of a tangent line at a specific point on a circle, the gradient of the radius and tangent must be calculated and substituted into the point-slope formula

### Tangent to a Circle with a Given Gradient

The equation of a tangent line can be found by using the point-slope formula with the given gradient of the tangent and a point on the circle

### Solving Geometric Problems Involving Tangents

A systematic approach of calculating the gradient of the radius, tangent, and using the point-slope formula is crucial for solving problems involving tangents to circles

Algorino

Edit available