Chord (of a circle)
A segment that connects two different points on a circle’s circumference.
In geometry, a chord of a circle is a straight line segment that connects two points on the circle. It is the largest segment that can be drawn inside a circle, and its endpoints lie on the circle itself. The chord divides the circle into two segments, one on each side of the chord.
The center of the circle lies on the perpendicular bisector of the chord. This means that the segment connecting the center of the circle with the midpoint of the chord is perpendicular to the chord and bisects it.
The length of a chord can be calculated using the following formula:
Chord length = 2 × radius × sin (angle/2)
where radius is the distance from the center of the circle to any point on the circle, and angle is the angle formed by the endpoints of the chord at the center of the circle.
Chords are important in geometry as they are used to identify and describe many geometric figures, such as triangles, quadrilaterals, and polygons inscribed in circles. Chords also play a key role in the definition of tangents, secants, and arcs of circles.
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