Chord of Circle

The chord of the circle is a line segment that connects two places on the circle’s circumference. The chord is one of the many line segments that can be drawn in a circle, with its endpoints on the circumference. A chord is a piece of a line that joints any two points on a circle. The circle’s circumference contains the endpoints of these line segments.  The Chord that passes through the centre of the circle is known as the Diameter. The word “chord” comes from the Latin word “chorda,” which literally means “bowstring.

Circle’s Different Components

Centre: The centre of a circle is the place inside the circle from which the distances to the points on the circumference are equal.

Radius: The radius of a circle is a line segment that connects the circle’s centre to any point on its circumference.

Diameter: The diameter of a circle is the line segment that begins at any point on the circumference of the circle, passes through the centre, and ends at the opposite side of the circle’s circumference.

Circumference: The circumference of a circle is the circumference of the circle’s boundary.

Semicircles: A half-circle is referred to as a semicircle. A diameter is the distance between two semicircles in a circle.

Chord of circle

A circle’s chord is a line segment connecting any two points on the circle. The circle’s circumference is where the line segments’ termination are located. The Secant is the Chord’s extension.

 PQ. A chord that goes through the centre of the circle is also known as a diameter.

Circle’s Chord Properties 

A few key properties of a circle’s chords are listed below.

• The chord is bisected by the perpendicular to a chord drawn from the circle’s centre.

• The chords of a circle that are equidistant from the circle’s centre are equal.

• The only circle that goes through three collinear points is the one and only circle.

• When a circle chord is drawn, it divides the circle into two sections, which are referred to as the major and minor segments of the circle.

• When a chord is prolonged indefinitely on both sides, it is called a secant.

Chord of a circle formula

The length of a chord can be calculated using two formulas. Each formula is applied based on the data provided.

• Given the radius and distance to the centre of a circle, the length of a chord.

If you know the radius length and the distance between the centre and the chord, you can use the formula to get the chord length.

Length of chord = 2 √ r2-d2

• Given the radius and central angle, the length of a chord

The length of a chord is determined by, if the radius and central angle of a chord are known.

Length of a chord = 2 × r × sine (C/2)

= 2r sine (C/2)

Where,  r denotes the circle’s radius.

C = the chord’s subtended angle at the middle

d is the perpendicular distance between the circle’s centre and the chord.

Chord of a Circle Theorems

Theorem 1: The chord is bisected by a perpendicular drawn from the circle’s centre.

To understand the theorem, consider the a circle, in which OP is the perpendicular bisector of chord AB and the chord is bisected into AP and PB. As a result, AP = PB.

Theorem 2: The chords of a circle that are equidistant from the circle’s centre are equal.

To understand the theorem, look at the circle below, where chord AB Equals chord CD and they are equidistant from the centre if PO = OQ.

Theorem 3: In a circle with two unequal chords, the larger chord is closer to the centre than the smaller chord. 

When we draw many chords in a circle from the diameter to both ends, we will notice that the chord lengthens as we get closer to the centre.

Conclusion

In this article we learn, the chord is bisected by the perpendicular to a chord drawn from the circle’s centre. The chords of a circle that are equidistant from the circle’s centre are equal. The only circle that goes through three collinear points is the one and only circle. . The chord is a straight line that connects two locations on a circle’s circumference. Because it connects two places on the perimeter of a circle, the diameter of a circle is called the longest chord.