A circle is a curved plane figure. Every point on the circle is equidistant from a fixed point known as the center of the circle. It is a 2D shape and is measured in terms of radius. The word ‘Circle’ is derived from the Latin word 'circulus' meaning small ring.
|1.||What is Circle?|
|2.||Parts of a Circle|
|3.||Properties of Circle|
|5.||FAQs on Circles|
What is Circle?
A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Parts of a Circle
There are many parts or components of a circle that we should know to understand its properties. A circle has mainly the following parts:
Circumference: It is also referred to as the perimeter of a circle and can be defined as the distance around the boundary of the circle.
Radius of Circle: Radius is the distance from the center of a circle to any point on its boundary. A circle has many radii as it is the distance from the center and touches the boundary of the circle at various points.
Diameter: A diameter is a straight line passing through the center that connects two points on the boundary of the circle. We should note that there can be multiple diameters in the circle, but they should:
- pass through the center.
- be straight lines.
- touch the boundary of the circle at two distinct points which lie opposite to each other.
Chord of a Circle: A chord is any line segment touching the circle at two different points on its boundary. The longest chord in a circle is its diameter which passes through the center and divides it into two equal parts.
Tangent: A tangent is a line that touches the circle at a unique point and lies outside the circle.
Secant: A line that intersects two points on an arc/circumference of a circle is called the secant.
Arc of a Circle: An arc of a circle is referred to as a curve, that is a part or portion of its circumference.
Segment in a Circle: The area enclosed by the chord and the corresponding arc in a circle is called a segment. There are two types of segments - minor segment, and major segment.
Sector of a Cirlce: The sector of a circle is defined as the area enclosed by two radii and the corresponding arc in a circle. There are two types of sectors - minor sector, and major sector.
For better understanding observe the given image depicting all parts of a circle.
Properties of Circle
Let us move ahead and learn about some interesting properties of circles that make them different from other geometric shapes. Here is a list of properties of a circle:
- A circle is a closed 2D shape that is not a polygon. It has one curved face.
- Two circles can be called congruent if they have the same radius.
- Equal chords are always equidistant from the center of the circle.
- The perpendicular bisector of a chord passes through the center of the circle.
- When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points.
- Tangents drawn at the endpoints of the diameter are parallel to each other.
Let's see the list of important formulae pertaining to any circle.
- Area of a Circle Formula: The area of a circle refers to the amount of space covered by the circle. It totally depends on the length of its radius → Area = πr2 square units.
- Circumference of a Circle Formula: The circumference is the total length of the boundary of a circle → Circumference = 2πr units.
- Arc Length Formula: An arc is a section (part) of the circumference. Length of an arc = θ × r. Here, θ is in radians.
- Area of a Sector Formula: If a sector makes an angle θ (measured in radians) at the center, then the area of the sector of a circle = (θ × r2) ÷ 2. Here, θ is in radians.
- Length of Chord Formula: It can be calculated if the angle made by the chord at the center and the value of radius is known. Length of chord = 2 r sin(θ/2). Here, θ is in radians.
- Area of Segment Formula: The segment of a circle is the region formed by the chord and the corresponding arc covered by the segment. The area of a segment = r2(θ − sinθ) ÷ 2. Here, θ is in radians.
Check these interesting articles related to circles in math.
Examples on Circles
Example 1: If the radius of a circular pool is 20 units. What is the length of the diameter of the pool?
Given: Radius = 20 units ⇒ Diameter of pool (circle) = 2 × r. Therefore, the length of the diameter of circular pool = 2 × 20 = 40 units.
Example 2: John went swimming in a circular swimming pool. After swimming, he ran one round along the boundary of the pool. If the radius of the pool is 35 feet, can you find the distance that John ran around the pool?
To find the distance that John ran, we need to know the circumference of the circle (pool). For this, we need to know the value of π and r, where r is the radius of the pool. Given: r = 35 feet, and π = 22/7. Using the formula, Circumference (C) = 2πr ⇒ C = 2 × 22/7 × 35 = 220 feet. Therefore, John ran 220 feet.
Example 3: You want to decorate your tabletop, which is in the shape of a circle, with a colorful sticker. If the radius of the tabletop is 21 inches, find the amount of paper you need to cover its top surface.
Given: r = 21 inches, π = 22/7. Using the formula, Area = πr2 ⇒ A = 22/7 × 21 × 21 = 1386 square inches. Therefore, the area of a table top is 1386 square inches.
FAQs on Circles
What is a Circle in Geometry?
A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'. One of the best examples of the circle in the real world is a pizza base.
How Circle is Two-Dimensional?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is at the same distance from the center of the circle. Its real-life examples include flat surfaces or pictures of wheels, pizzas, orbit, etc.
What are the Formulas of Circles?
Formulas related to circles are:
- Diameter of a Circle ⇒ D = 2 × r units.
- Circumference ⇒ C = 2 × π × r units.
- Area ⇒ A = π × r2 square units.
What is a Half-Circle called in Geometry?
In geometry, a semicircle refers to the half of a circle. The diameter divides the circle into two equal parts that are semi-circles.
What is a Chord in a Circle?
A chord is the line segment joining two points inside a circle on its arc. As the diameter also having two endpoints on a circle, so, it is the longest chord. All angles marked in the circle subtended by the same chord are equal.
What are the Major Parts of a Circle?
The list of the different parts of a circle includes tangent, chord, radius, diameter, minor arc, major arc, minor segment, major segment, minor sector, and major sector.
What is the Circumference of a Circle?
The circumference of a circle is defined as the linear distance around its boundary or we can say, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
What are the Properties of Circles?
Following are some of the properties of circles:
- The two circles with equal radius are congruent in nature.
- The diameter is the longest chord of a circle and it divides the circle into two equal parts.
- The radius of the circle bisects the chord if it is drawn perpendicular to the chord.