Table of Contents
Radius of a Circle Definition
The radius of a circle is the distance from the center of the circle to any point on the circle.
The Diameter of a Circle is the length of the line that starts from one point on a circle to another point and passes through the centre of the circle, and it is equal to twice the radius of the circle. It is denoted by ‘d’ or ‘D’.
The radius of a circle is the distance from its centre to any point on its edge, and it is equal to half the diameter of the circle. It is denoted by ‘r’ or ‘R’.
The circumference of a circle is the distance around the edge of the circle, and it is equal to 3.14 times the radius of the circle. It is denoted by ‘C’.
Definition of the Radius of a Circle and the Chord
The radius of a circle is the distance from the center of the circle to its edge. The chord is a line segment that connects two points on a circle.
Length of Chord of Circle Formula
The length of chord of a circle is the distance between two points on the circumference of the circle. This distance can be found using the following formula:
- Chord length = circumference ÷ (2 × pi)
- where pi is a constant equal to 3.14159.
What is a Circle?
A Circle is a plane figure with all points on it equidistant from a common point within it.
Define Radius of a Circle
A radius of a circle is the distance from the center of the circle to its edge.
Define Relation Between Radius of a Circle and Chord
A chord is a line segment that connects two points on a circle. The radius is the length of the line segment from the center of the circle to the chord.
Chord of a Circle Theorems
There are three theorems associated with chords of a circle.
- The first is the theorem of perpendicularity, which states that the perpendicular bisector of a chord intersects the chord at its midpoint.
- The second is the theorem of equality of angles, which states that the angles at the points of intersection of two chords are equal.
- The third is the theorem of subtraction, which states that the angle between a chord and the tangent at its point of intersection is equal to the angle between the chord and the radius.
Theorem 1:
If \(p\) is a prime number and \(a\) is a natural number, then \(p\) divides \(a\) if and only if \(p\) is a factor of \(a\).
Proof:
We will show that \(p\) divides \(a\) if and only if \(p\) is a factor of \(a\).
If \(p\) divides \(a\), then \(p\) is a factor of \(a\).
If \(p\) is a factor of \(a\), then \(p\) divides \(a\).
Theorem 2:
If a and b are positive integers, then their product a×b is also a positive integer.
Proof:
We will use the well-ordering principle to show that a×b is a positive integer.
Suppose a×b is not a positive integer. This means there exists a positive integer c such that a×b < c. But then a×b – c is a negative integer, which is impossible. Therefore, a×b is a positive integer.
Length of Chord of Circle Formula
The length of the chord of a circle is the length of the line segment that connects the points of the circle that are the endpoints of the chord. The length of a chord can be found using the following formula:
The length of a chord is given by the following equation:
where “r” is the radius of the circle and “d” is the distance between the endpoints of the chord.
What is an Arc and Chord of a Circle?
An arc is a portion of the circumference of a circle. A chord is a line segment that connects two points on a circle.
