# Chord of a Circle

How to use the property of the chord of a circle: definition, property, 1 example, and its solution.

## Definition

A chord is a line segment

whose endpoints are on the circle.

## Property

If a line segment

starts from the center of the circle

(or passes through the center)

and is perpendicular to the chord,

then the line segment bisects the chord.

## Example

Solution

Solution (Detail)

OP starts from the center of the circle.

And OP is perpendicular to the chord AB.

Then OP bisects AB.

So AP = PB.

OC is the radius.

OC = 5

OA is also the radius.

So OA = 5.

See △APO.

It's a right triangle.

The sides are (3, AP, 5).

So this right triangle is

a (3, 4, 5) right triangle.

Pythagorean Triple

So AP = 4.

AP = 4

AP = PB

So BP = 4

AP = BP = 4

AB = AP + PB

So AB = 4 + 4 = 8.

So 8 is the answer.