# Tangent to a Circle

How to use the properties of the tangent to the circle: definition, 2 properties, 2 examples, and their solutions.

## Definition

### Definition

A tangent to a circle is a line

that touches the circle.

From a point exterior of the circle,

you can draw two tangents.

## Property 1

### Property

The tangent and the radius

are perpendicular

at the intersecting point of the circle.

## Example 1

### Example

### Solution

Ray PB is tangent to the given circle

at point B.

And OB is the radius.

So ray PB and OB are perpendicular.

OB is the radius.

OB = 5.

OA is also the radius.

So OA = 5.

See △OPB.

It's a right triangle.

The sides are (5, PB, 8 + 5) = (5, PB, 13).

So this right triangle is

a (5, 12, 13) right triangle.

Pythagorean Triple

So PB = 12.

So write 12.

So 12 is the answer.

## Property 2

### Property

If two segments from an exterior point

are tangent to a circle,

then those two segments are congruent.

## Example 2

### Example

### Solution

The blue segments

start from the same point A.

They are tangent to the same circle.

So the blue segments are congruent:

7.

The green segments

start from the same point B.

They are tangent to the same circle.

So the green segments are congruent:

10.

The brown segments

start from the same point C.

They are tangent to the same circle.

So the brown segments are congruent:

5.

See △ABC.

There are 2 of 7, 10, and 5.

So the perimeter is

P = 2(7 + 10 + 5).

7 + 10 + 5 = 22

2⋅22 = 44

So 44 is the answer.