110 LearnersLast updated on August 13th, 2025
Properties of Circle
A circle is a fundamental shape in geometry that possesses unique properties. These properties help students simplify geometric problems related to circles. The properties of a circle include a constant distance from the center to any point on its circumference, known as the radius, and the relationship between the radius and other elements like the diameter and circumference. These properties assist students in analyzing and solving problems related to symmetry, angles, and area. Now let us learn more about the properties of a circle.
What are the Properties of a Circle?
The properties of a circle are simple, and they help students understand and work with this essential shape. These properties are derived from the principles of geometry. There are several properties of a circle, and some of them are mentioned below: Property 1: Radius Every point on the circle is equidistant from its center, and this distance is called the radius. Property 2: Diameter The diameter is twice the radius and is the longest chord that passes through the center. Property 3: Circumference The circumference is the distance around the circle, calculated as 2π times the radius. Property 4: Area Formula The formula used to calculate the area of a circle is given below: Area = πr² Here, r represents the radius of the circle. Property 5: Central Angle All central angles of a circle add up to 360 degrees.
Tips and Tricks for Properties of a Circle
Students tend to confuse and make mistakes while learning the properties of a circle. To avoid such confusion, we can follow the following tips and tricks: Understanding Radius and Diameter: Students should remember that the diameter is always twice the radius. To verify this, students can measure or draw a circle and see that the diameter spans across the center. Knowing the Formula for Circumference: Students should remember the formula for circumference, which is 2π times the radius. Calculating Area Accurately: Students should practice using the area formula, Area = πr², and understand that r is the radius. Symmetry and Central Angle: Students should remember that a circle has rotational symmetry and all central angles sum to 360 degrees.
Confusing Radius and Diameter
Students should remember that the diameter is twice the radius and not equal to it.
Mistake 1
Misinterpreting the Circumference Formula
Students should know and remember that the circumference is calculated as 2π times the radius.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice the formula used to find the area of a circle, which is given below. The students must also understand that r represents the radius. Area = πr²
Mistake 3
Misunderstanding Central Angle Sum
Students should remember that all central angles in a circle add up to 360 degrees.
Mistake 4
Forgetting the Constant Radius Rule
Students must remember that all points on the circumference are equidistant from the center, defining the radius.
Mistake 5
Solved Examples on the Properties of Circles
In a circle, the radius is 5cm. What is the diameter of the circle?
Diameter = 10cm.
Problem 1
The diameter is twice the radius. Since the radius is 5cm, then the diameter = 2 x 5 = 10cm.
In a circle with a radius of 7cm, what is the circumference?
Explanation
Circumference = 44cm (approximately).
Problem 2
The circumference is calculated using the formula 2πr. Substitute r = 7 into the formula: Circumference = 2 x π x 7 ≈ 44cm.
A circle has a radius of 3cm. What is its area?
Explanation
Area = 28.27 sq cm (approximately).
Problem 3
The area of a circle is calculated using the formula πr². Substitute r = 3 into the formula: Area = π x 3² = 28.27 sq cm (approximately).
If the diameter of a circle is 16cm, what is the radius?
Explanation
Radius = 8cm.
Problem 4
The radius is half of the diameter. Since the diameter is 16cm, the radius = 16/2 = 8cm.
If a central angle in a circle is 90 degrees, what fraction of the circle's circumference does it subtend?
Explanation
The central angle subtends 1/4 of the circumference.
A circle is a shape consisting of all points in a plane that are at the same distance from a given point called the center.
1.How many radii are there in a circle?
2.Are all diameters of a circle equal?
3.How do you find the area of a circle?
4.Can a circle have corners or edges?
Common Mistakes and How to Avoid Them in Properties of Circles
Students tend to get confused when understanding the properties of a circle, and they tend to make mistakes while solving problems related to said properties. Here are some common mistakes students tend to make and the solutions to said common mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
