# Tangent to a Circle

How to solve the tangent to a circle problems: definition, properties, examples, and their solutions.

## Definition

A tangent to a circle is a line

that touches the circle.

A tangent and a circle have one intersecting point.

From a point that is exterior of the circle,

you can draw two tangents.

## Property 1

The tangent and the radius are perpendicular

at the intersecting point of the circle.

## Example 1

The radius is 5.

So the distance between point *A*

and the center of the circle is 8 + 5, 13.

The blue tangent and the radius

are perpendicular at point *B*.

So the given triangle is a right triangle.

The hypotenuse is 13.

And the leg is 5.

So the triangle is a (5, 12, 13) right triangle.

So *x* = 12.

## Property 2

If two segments from an exterior point

are tangent to a circle,

then those two segments are congruent.

## Example 2

The same colored segments

start from the same point,

and are tangent to the circle.

So the same colored segments are congruent.

So the perimeter *P* is:*P* = 2(7 + 10 + 5).

This is the way to find the perimeter

of the circumscribed polygon.