Chord of a Circle

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.

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

Property

If a line segment starts from the radius and is perpendicular to the chord, then the line segment bisects the chord.

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

Find AB. OC = 5, OP = 3. AB is the chord of the circle.

OA is the radius.
So OA = 5.

See △APO:
The hypotenuse is 5 and the leg is 3.
So it's a (3, 4, 5) right triangle.
So AP = 4.

OPAB (⊥: is perpendicular to)
So OP bisects AB.
So AP = PB = 4.

So AB = 4 + 4 = 8.