Area of Circle Proof
We can easily prove the formula for the area of the circle using the area of the triangle formula. For this first, we have to draw various concentric circles inside the given circle. Then open all the concentric circles to form a right-angled triangle.
If the radius of the given circle is r, then the outer circle would form the base of the right triangle having length 2πr.
Height of the triangle is ‘r’
Area of the right-angled triangle so formed is equal to the area of a circle.
Area of a Circle = Area of Triangle = (1/2) × base × height = (1/2) × 2π r × r
Therefore,
Area of Circle = πr2
Circles in Maths
Circles in Maths: A circle is a two-dimensional shape where all points on the circumference are the same distance from the centre. In other words, it is a collection of all points in a plane that are the same distance away from a fixed point, called the centre. Its area is equal to pi times the square of its radius.
In this article, you will understand more about circles in math, including their formulas, examples, parts of circles, and practice problems on circles.
Table of Content
- What is a Circle in Maths?
- Circle Definition
- Circle Examples
- How to Draw a Circle?
- Interior and Exterior of Circle
- Parts of Circle
- Center of Circle
- Radius of Circle
- Diameter of Circle
- Chord of Circle
- Tangent of Circle
- Secant of Circle
- Arc of a Circle
- Segment in Circle
- Sector of a Circle
- Properties of Circle
- Circle Formulas
- Area of Circle Proof
- Types of Circles
- Solved Examples on Circles
- Practice Problems on Circles in Maths
- MCQs on Circles in Maths