# How to Locate the Point of Tangency Between a Circle and a Line - Comprehensive Guide

Knowing how to locate the point of tangency between a circle and a line is a critical skill for many engineering and technical design problems. This tutorial will provide you with an easy-to-follow step-by-step guide to help you find the exact point of tangency between a circle and a line.

## What Is the Point of Tangency Between a Circle and a Line?

The point of tangency is the point along the circumference of a circle where the line tangents, or touches, the circle. This point can be a “tangent intersection”, which is when a single point exists on both the line and the circle, or a “tangent touchpoint”, which is when multiple points exist on the circle but the line only touches it at one particular point.

## How to Find the Point of Tangency

1. Draw the circle and line on your page
2. Identify the points of intersection between the line and the circle
3. Calculate the common points of the equation
4. Use the geometric properties of the circle and line to determine which point is the point of tangency

Let's look at an example:

In this example, our circle and line intersect at two different points. To determine which point is the point of tangency, we need to analyze the geometry of each point.

At point A, the line is perpendicular to the circle and therefore cannot be our point of tangency. At point B, the line is parallel to the circle and therefore is our point of tangency.

## FAQs

#### What Is the Point of Tangency?

The point of tangency is the point on the circumference of the circle where the line tangents the circle.

#### How Is the Point of Tangency Found?

The point of tangency can be found by drawing the circle and line on your page, identifying the points of intersection between the line and the circle, and using the geometric properties of the circle and line to determine which point is the point of tangency.

#### What Is a Tangent Intersection?

A tangent intersection is when a single point exists on both the line and the circle.

#### What Is a Tangent Touchpoint?

A tangent touchpoint is when multiple points exist on the circle but the line only touches it at one particular point.

#### What Are the Geometric Properties of a Circle and Line?

The geometric properties of a circle and line include the circle’s radius and circumference, and the slope of the line.

If you are looking for more information on circles in general, the Wikipedia page on circles is an excellent source of information to learn from.

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