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.

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.