Equation Of Chord

When you look at an object, you see a figure called a shape. This figure shows the object’s surface, boundaries, and lines. Everything in our environment comes in a variety of shapes and sizes. Consider yourself on one side of a circular lake, looking across to the opposite side’s fishing pier. The chord is the line that connects you and the fishing pier across the circle. The circumference of a lake is the circle that encircles its perimeter. A circle chord can connect two points on the circle’s circumference. The circumference of an object can be determined by using the equation of chord.

Circle

A circle is a complete round shape made up of all points on a plane that are a specified distance from another point. They are formed by a circular curved line encircling a central point. The points on the line are all equally spaced apart from the centre. The distance between the centre of a circle and its circumference is its radius.

What Is The Meaning Of A Chord?

A chord is a line segment that connects any two points in a circular path. The endpoints of these segments are located on the circle’s circumference. The circle’s diameter is defined by the chord that runs across its center. It is the largest chord that can be formed in a circle. A circle segment is an area between Chord and one of the Arcs.

On the other hand, a secant is a chord that extends beyond the circumference of the circle and is therefore not considered a chord at all.

Meaning of Chord of A Circle

An equation of chord meaning is defined as a straight line that connects two locations on the circle’s circumference. Because it relates to other areas on the circle’s perimeter, the diameter is considered the longest chord. A chord is a line segment whose ends are on the circumference of a circle. A diameter is a chord that runs across the circle’s center.

There are three chords in the circle below. 

The Features Of A Circle’s Chord

• To use the equation of chord, first, divide a chord in half by drawing a line perpendicular to it from the circle’s centre.

• Chords that are equidistant from the circle’s centre are equal.

• There will be only 1 circle that goes through 3 collinear points.

• A chord is extended continuously on both sides and forms a secant.

• A circle’s chord splits the circle into two sections, also referred to as the circle’s segments. These parts are called “minor” or “major” segments.

• Chords of the same length cover the same angles at the centre of a circle.

• When the chord’s subtended angles are equal, the chord’s length is identical.

Equations of Chord Calculation

There are two fundamental methods or formulas for calculating the chord length. First, the trigonometric method and perpendicular distance from the circle centre can be used to determine the equation of chord.

1. Using the radius and angle of the central axis

The equation of chord below calculates the length of a chord given the radius and central inclination angle.

Using trigonometry, the chord length = 2 × r × sin(c/2);

Where,

‘r’ indicates the radius.

‘c’ is the angle formed by the chord at the centre.

‘sin’ indicates the sine function.

2. Using the radius and distances to the center as parameters

The following is an equation of chord that may be used to determine the distance of a chord if the radius and perpendicular distances from the chord towards the circle centre are specified. Pythagoras’ Theorem is used here in a simple way.

Chord length when measured perpendicular to the centre = 2 × √ (r2 − d2)

Where,

‘r ‘denotes the radius of the circle.

‘d’ denotes the perpendicular distance between chord and circle centre

We know that the chord is divided by a perpendicular bisector that separates from the circle’s centre. So the chord is half of the right triangle.

By Using Pythagoras theorem,

(1/2 chord)2 + d2 = r2

=> 1/2 x Chord length = √(r2 − d2)

= > Chord length = 2 × √(r2 − d2)

Equation of chord Theorems

A circle’s chord is related to a few theorems.

• Theorem 1: A perpendicular bisector to a chord drawn from the circle’s center bisects it.

• Theorem 2: The chords that are equidistant from the circle’s center are equal.

• Theorem 3: For unequal circle chords, the larger chord is closer to the center.

Conclusion

Any two points, mainly on the circle’s circumference, can be connected together with a chord. The circle’s diameter, defined as the line segment passing through its center, is its longest chord. The length of a chord can be calculated using the Equation of chord. Additionally, you can determine chord length if we know the radius and the distance of the central axis, the distance between the circle’s center and the chord’s center.