The blue line in the figure above is called a "chord of the circle c". A chord is a lot like a secant, but where the secant is a line stretching to infinity in both directions, a chord is a line segment that only covers the part inside the circle. A chord that passes through the center of the circle is also a diameter of the circle.
Below is a formula for the length of a chord if you know the radius and central angle.
where
Below is a formula for the length of a chord if you know the radius and the perpendicular distance from the chord to the circle center.
This is a simple application of
Pythagoras' Theorem.
whereThe perpendicular bisector of a chord always passes through the center of the circle. In the figure at the top of the page, click "Show Right Bisector". Then move one of the points P,Q around and see that this is always so. This can be used to find the center of a circle: draw one chord and its right bisector. The center must be somewhere along this line. Repeat this and the two bisectors will meet at the center of the circle. See Finding the Center of a Circle in the Constructions chapter for step-by-step instructions.
If two chords of a circle intersect, the intersection creates four line segments that have an interesting relationship. See Intersecting Chord Theorem.