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.

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