Circles in Maths- Definition, Formulas, Properties, Parts

Circles: In geometry, Circle is a 2-dimensional shape in which all points in a plane are at a specific distance from a specific point in the center. There are numerous examples of Circles in our daily lives. Coins, Discs, Bangles, wheels, rings, etc are examples of circles. Let us learn more about the circle definition, circle formulas, and the many sections of a circle by working through some circle practice problems on this page.

Circle

The term “circle” comes from the Latin word “circulus,” which means “small ring.”A circle is a two-dimensional shape made by a set of points on the plane that are separated by a specified distance (radius). The fixed point is known as the origin or center of the circle, and the fixed distance between the points is known as the radius. The radius of a circle is the distance between any two points on the circle. Typically, the radius must be a positive integer.Check out the accompanying diagram to see how a circle is made up of its center, radius, and diameter.

Circle Shape Objects

In our daily lives, we encounter various objects whose shape is circular. In shape. Check out some examples of a Circle. 

• Ball
• Round wall Clock 
• Tyre
• Coins
• Wheels
• Rings
• Buttons
• CDs
• Bangles
• Plates

Parts of a Circle

A circle is a closed two-dimensional figure with a curved side whose ends meet to form a round shape and all points in the plane are equidistant from a fixed point called “center” Beside Radius and. center there are various types of parts present in a circle. Let’s take a look at the parts of a Circle;

Center of a Circle: The center of a circle is the middile point from which any point on the perimeter of the circle is always present at a set distance.

Radius: The radius of a circle is the distance between any point on the circle’s circumference and the fixed point known as the center. The letter ‘r’ is used to represent it. 

Diameter of a Circle:: A diameter of a circle is a straight line that passes through the center and connects two locations on the circle’s boundary. The Diameter is always twice as large as the Radius. The letter ‘D’ represents it. The radius and the center have the following relationship:

D= 2r

Chord of a Circle: A chord is any line segment that touches the circle at two different locations on its boundary. A circle’s diameter is its largest chord. This cuts through the middle and divides it into two equal portions.

Arc of a Circle: An arc is a portion of a circle that has all of its points on the circle. It is a curved portion of its circumference. that joins the diameter’s endpoints has a measure of 180°

Secent of a Circle: The secant is a straight line that crosses two locations on an arc/circumference of a circle. It’s also known as an extended chord.

Tangent of a Circle:  A coplanar straight line that intersects the circle at a single point but lies outside of it.

Circle Segment: The chord divides the circle into two sections, each of which is referred to as a circle segment.  Segments come in two varieties: minor segments and big segments.

Sector of a Circle: The region contained by two radii and the associated arc in a circle is known as the sector of a circle. Minor and large sectors are the two different categories of sectors.

Circles formulas

The circle has several formulas, including the area and perimeter of the circle. The area of a circle is defined as the space occupied inside the circle’s boundary, and the circumference of a circle is the length of the circle’s boundary. These Circle formulas are very useful to find out any area and properties of any circular object. Check out the major Circle formulas given below.

Circumference of a Circle 

We earlier came to know that a circle is a round close shape in a 2-dimensional plane. The measurement of the circle’s boundaries is known as the circumference or perimeter of the circle. In simple words, the circumference is the complete length of a circle’s boundaries. We can find out the circumference of any Circle using the following formula.

Circumference of a Circle = 2πr, [where ‘r’ is the radius and π= 3.14]

Area of a Circle

Area of a Circle The area of any circle is defined as the area that’s surrounded by the circle or the space covered by the circle. The area of a circle is entirely determined by the length of its radius. The area of a circle is commonly denoted as ‘A’. The formula for calculating the area of a circle is as follows: 

Area of a circle = A = πr2, [where ‘r’ is the radius and π = 3.14]

Properties of a Circle

Let us now look at some of the most important properties of circles, which are listed below.

• A circle is a closed two-dimensional form with one curved face.
• The circle’s diameter is the largest chord and is twice the radius.
• The circle’s diameter divides it into two equal sections.
• Tangents drawn from the diameter’s endpoints are always parallel to each other.
• A chord’s perpendicular bisector runs across the center of the circle.
• Circles with equal radii are congruent to one another.
• When two circles overlap, the line connecting the intersecting points is perpendicular to the line connecting the centers of the circles.

Sharing is caring!