Theorems of circle Class 9

In this article you will find out the Theorem of Class 9 from the Chapter 10 Circle. We hope that this will help you to gain extra marks in your examination.

Some Important Points about Circle

A circle is a geometric shape that consists of all points in a plane that are a fixed distance, called the radius, away from a central point called the center. Here are some theorems about circles that are typically taught in a high school geometry class:

1. The diameter of a circle is a straight line that passes through the center of the circle and has its endpoints on the circle. The diameter is twice the radius of the circle.
2. The circumference of a circle is the distance around the circle. It is equal to 2π times the radius of the circle, where π is a mathematical constant approximately equal to 3.14.
3. The area of a circle is the amount of space inside the circle. It is equal to π times the radius squared.
4. Two chords of a circle that are equidistant from the center of the circle are congruent.
5. A line that passes through the center of a circle and touches the circle at only one point is called a radius. All radii of a circle are congruent.
6. A line that is drawn through the center of a circle and intersects the circle at two points is called a diameter. All diameters of a circle are congruent.
7. The length of an arc is proportional to the measure of the central angle formed by the arc.
8. A tangent to a circle is a line that touches the circle at only one point, called the point of tangency.

Circle Theorems and Proofs Class 9

Theorem 1. Equal chords of a circle subtend equal angles at the centre.

Sol.

Theorem 2. If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Sol.

Theorem 3. The perpendicular from the center of a circle to a chord bisects the chord.

Sol.

Theorem 4. The line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

Sol.

Theorem 5. There is one and only one circle passing through three given non-collinear points.

Sol.

Theorem 6. Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

Sol.

Theorem 7. Chords equidistant from the centre of a circle are equal in length.

Sol.

Theorem 8. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Sol.