Cambridge O Level Additional Mathematics · Syllabus 4037 · Coordinate Geometry of the Circle
Chord of a Circle
What is Chord of a Circle?
A straight line segment whose two endpoints both lie on a circle. A line drawn across a circle produces a chord exactly when it meets the circle at two distinct points, which happens when substituting the line into the circle equation yields a quadratic with a positive discriminant, or equivalently when the perpendicular distance from the centre to the line is less than the radius. The longest possible chord is a diameter, which occurs when the line passes through the centre so that this distance is zero. The length of a chord at perpendicular distance d from the centre of a circle of radius r is two times the square root of r squared minus d squared, and the perpendicular from the centre to a chord always bisects it.
This definition is part of the Coordinate Geometry of the Circle chapter in Cambridge O Level Additional Mathematics.