Circles
We see circles everywhere, wheels, clocks, plates, coins, and even bubbles! But what exactly is a circle? In math, circles are very important shapes. They may look simple, but they have some amazing properties and rules.
In this blog, we will define circle, learn what is a circle, understand how circles work, explore properties, theorems, and discover how circles show up in real life.
Whether you're just starting or want a fun refresh, this guide to circles makes everything easy and exciting.
Table of Contents
- What is a Circle?
- Define Circle in Math
- Parts of a Circle
- What is the First Circle Called?
- What are the 7 Properties of a Circle?
- What are the 14 Theorems of Circles?
- What Are 5 Circles Examples?
- Why Are Circles Important?
- Fun Circle Facts
- Conclusion
- FAQs on Circles
What is a Circle?
Let’s begin by answering the most basic question: What is called a circle?
A circle is a closed curved shape where every point on the curve is the same distance from the centre point. This fixed distance is called the radius.
In simple words, if you tie a pencil to a string and draw around a fixed point without changing the length of the string, you make a circle.
Define Circle in Math
In mathematics, we define a circle as:
A set of all points in a plane that are at a fixed distance (called the radius) from a fixed point (called the centre).
So, a circle is not just any round shape it has a specific rule that all points must follow.
Parts of a Circle
To understand circles better, let’s look at some important parts:
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Centre – The fixed point in the middle.
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Radius – The distance from the centre to any point on the circle.
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Diameter – A straight line passing through the centre, touching two points on the circle. It’s twice the radius.
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Circumference – The boundary or the outer line of the circle.
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Chord – A line that connects two points on the circle (not always through the centre).
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Arc – A part of the circumference.
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Sector – A "pizza slice" shaped part of the circle.
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Segment – The part between a chord and an arc.
What is the First Circle Called?
In basic geometry, we don’t really name the first circle. But in historical or philosophical contexts, the first circle might refer to:
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The unit circle – a special circle in math with a radius of 1, centred at the origin.
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Or in ancient astronomy, the celestial sphere was sometimes called the "first circle."
But in geometry for students, the unit circle is often the first circle we learn about.
What are the 7 Properties of a Circle?
Here are 7 important properties of a circle:
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All points on the circle are equidistant from the centre.
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The diameter is twice the radius.
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The longest chord of a circle is its diameter.
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A radius drawn perpendicular to a chord bisects the chord.
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Equal chords are equidistant from the centre.
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A tangent to a circle is perpendicular to the radius at the point of contact.
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The angle in a semicircle is always a right angle (90°).
These properties help us solve many geometry problems related to circles.
What are the 14 Theorems of Circles?
Here are 14 key theorems of circles (simplified for easier understanding):
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Equal chords have equal distances from the centre.
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Chords equidistant from the centre are equal.
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The perpendicular from the centre to a chord bisects the chord.
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The line drawn through the centre to the midpoint of a chord is perpendicular to the chord.
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Only one circle can pass through three non-collinear points.
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The angle subtended by an arc at the centre is double the angle at any point on the remaining arc.
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Angles in the same segment are equal.
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The angle in a semicircle is 90°.
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Opposite angles of a cyclic quadrilateral are supplementary.
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Equal arcs subtend equal angles at the centre.
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Arcs subtending equal angles at the centre are equal.
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The tangent at any point on the circle is perpendicular to the radius at that point.
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From an external point, two tangents drawn to a circle are equal in length.
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The angle between the tangent and chord through the point of contact equals the angle in the alternate segment.
These theorems are especially useful when solving problems in high school geometry.
What Are 5 Circles Examples?
Here are 5 real-life examples of circles:
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Clock Face – The circular shape that shows the time.
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Coins – Round currency like pennies or rupees.
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Plates – Dinner plates and saucers are usually circular.
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Wheels – From cars to bicycles, wheels are perfect circles.
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Manhole Covers – Always round to prevent them from falling in!
These examples show how common and useful circles are in everyday life.
Why Are Circles Important?
Circles are everywhere in real life and math. Understanding them helps us:
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Measure curved paths (using circumference).
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Cover round areas (using the area of a circle).
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Design and build round objects in engineering.
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Understand waves, rotations, and motions in science.
From art to architecture to space science, circles play a huge role!
Fun Circle Facts
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π (Pi) is the special number used to calculate the circumference and area of a circle.
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The area of a circle is calculated by the formula: A = πr²
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The circumference of a circle is found using: C = 2πr
Conclusion
While a circle might look like a basic object, it contains numerous amazing facts, beautiful theorems, and intriguing applications.
Understanding why matters such as circles are important, not just in mathematics but in real life, shows how you’ve advanced from learning to define a circle to discovering what combines the elements together. Applying this understanding to geometry, with all its properties and theorems regarding circles, will make answering geometric questions effortless.
Related Sections
Pythagoras Theorem - Unlock the magic of right-angled triangles with the Pythagoras Theorem!
Point and Lines - Understand the basics of geometry by exploring points, lines, and line segments.
Two-Dimensional Shapes - Discover the world of 2D shapes - from triangles to hexagons!
Frequently Asked Questions on Circles
What is called a circle?
A circle is a shape where all points are the same distance from the centre. It is a closed curve with no corners or straight sides.
What are the 7 properties of a circle?
The 7 key properties include equal distance from the centre, equal chords, the diameter being the longest chord, and more. (See full list above.)
What are the 14 theorems of circles?
14 theorems describe the properties of chords, arcs, angles, tangents, and more in a circle. These help solve geometric problems.
What are 5 circles examples?
Clock, coin, plate, wheel, and manhole cover are common circular shapes in everyday life.
What is the first circle called?
The unit circle is often considered the first important circle in mathematics, especially in trigonometry.
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