# Chord of a Circle

How to solve the chord of a circle problems: definition, property, 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 radius

(or passes the radius)

and is perpendicular to the chord,

then the line segment bisects the chord.

## Example

The radius of the circle is 5.*OA* is the radius.

So *OA* = 5.

See △*OAP*.

It's a right triangle.

And starting from the shortest side,

the sides are (3, *AP*, 5).

So △*OAP* is a (3, 4, 5) right triangle.

Pythagorean triples

So *AP* = 4.

*OP* is perpendicular to *AB*,

which is the chord of the given circle.

So *OP* bisects *AB*.

So *AP* = *PB* = 4.

So *AB* = 4 + 4.

4 + 4 = 8

So *AB* = 8.