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.