Chord of a Circle

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

Definition

Definition

A chord is a line segment
whose endpoints are on the circle.

Property

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

Example

Solution

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.