A circle is a two-dimensional closed shape where a set of all points when fixed in a plane are equally spaced from its boundary. The center of the circle is the fixed point that contains equidistant from the boundary or the perimeter of the circle.
In this article, Edureify brings the definition and theorems of Circle. But before going into the definition of the chord of a circle, here are certain terms that are important to understand related to a circle-
- Centre– The middle point of the circle that is equidistant from the boundary of the circle from all points is the center of the circle.
- Diameter- the diameter is the straight line that passes through the center of the circle and its end touches the boundary of the circle
- Circumference- The circumference is the distance surrounding circle, also known as the perimeter. Read Edureify’s article on the Circumference of Circle to know more about the same.
- Radius– Radius is also a straight line drawn from the center of the circle, but only on one side. Radius is one of the most important features needed to calculate anything related to a circle.
- Pi– A very vital and key component of circles that helps in calculating their area and circumference is Pi. Pi’s value is determined by the ratio of the circle’s circumference to the diameter.
Chord of a Circle
The chord of a circle is a line that joins any two points on the circumference of the circle. One must note that the diameter is the longest chord of a circle that passes through the center of the circle.
In the above figure, O is the center of the circle. The line crossing through the center, O, of the circle is the diameter of the circle, the longest chord of the circle. The line below the diameter is another chord of the circle.
Properties of the chord of a circle
The following are some important properties of the chord of a circle-
- The perpendicular line drawn from the center of a circle bisects the chord
- The chords of a circle that are equidistant from the center of a circle are equal
- When a chord is drawn in a circle it divides the circle into two parts called segments- major segment and minor segment
- When a chord is extended infinitely on both ends, it becomes a secant
How to calculate the Chord of a Circle?
Here are the two basic formulas to calculate the chord of a circle-
- Calculating the length using the perpendicular distance from the center-
Chord Length = 2×√(r2- d2)
- Chord length using Trignometry-
Chord Length= 2×r×sin(c/2)
Example of Calculating the Chord of a Circle
Example 1-
Calculate the chord of a circle where: r= 7cm and the perpendicular distance from the chord is 4cm
Solution:
r= 7cm and distance d= 4cm
Chord Length= 2×√(r2- d2)
= 2×√(7×7-4×4)
=2×√(49-16)
=2√33
=2×5.744
= 11.48 cm
Therefore, the length of the chord is 11.48cm
Here was the definition and formula for calculating the chord of a circle.
Edureify has a particular section dedicated to maths. Students can learn and practice formulas and more with Edureify, the best AI learning App.
Some FAQs about the Chord of a Circle-
Q.) What is the chord of a circle?
The chord of a circle is a line that joins any two points on the circumference of the circle.
Q.) Is the diameter a chord of a circle?
Yes, the diameter is the longest chord of a circle.
Q.) What are the formulas for calculating the chord of a circle?
The formulas for calculating the chord of a circle are-
- Calculating the length using the perpendicular distance from the center-
Chord Length = 2×√(r2- d2)
- Chord length using Trignometry-
Chord Length= 2×r×sin(c/2)
Q.) What is the r in the formula for calculating the chord of a circle?
r stands for the radius of the circle in the formula of calculating the chord of a circle.
Q.) From where can I learn more formulas for maths?
Edureify! Edureify has a particular section dedicated to maths that will help students learn and practice maths.
