Properties of Chords of a Circle
There are various properties of chords in a circle, some of those properties are as follows:
- A chord that passes through the centre of a circle is called a diameter, and it is the longest chord in the circle.
- The perpendicular to a chord, that is drawn from the centre of the circle bisects the chord.
- Chords that are equidistant from the centre of a circle are equal in length.
- There is only one circle that passes through three collinear points.
- Chords that are equal in length subtend equal angles at the centre of a circle.
- The perpendicular bisector of a chord passes through the centre of the circle.
- If a radius is perpendicular to a chord, then it bisects the chord and the arc it intercepts. This is known as the perpendicular bisector theorem.
- When the subtended angles by a chord are equal then the length of chords are also equal.
- If two chords in a circle intersect, then the product of the segments of one chord is equal to the product of the segments of the other chord. This is known as the intersecting chords theorem.
- The angle subtended by a chord at the centre is twice the angle subtended by the chord at the circumference.
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Chords of a Circle
Chord of a circle is the line that joints any two points on the circumference of the circle. A circle can have various chords and the largest chord of a circle is the diameter of the circle. We can easily calculate the length of the chord using the Chord Length Formula. As the name suggests it is the formula for calculating the length of the chord in a circle in Geometry.
In this article, we will learn about the definition of the chord, theorems of the chords and the circle, explain its properties, and the formulas to calculate the length of the chord using different methods. The article also has some solved sample problems for better understanding.
Table of Content
- Circle Definition
- Chord of a Circle Definition
- What is Chord Length Formula?
- Chord of a Circle Theorems
- Properties of Chords of a Circle
- Solved Probelms
- FAQs