Circle formulas in math | Area, Circumference, Sector, Chord, Arc of Circle

Table of Contents

Properties of circle in math | Arc, Perimeter, Segment of circle

A circle can be defined as, it is the locus of all points equidistant from a central point. In this we discuss about Properties of circle, circle formulas like area, perimeter, arc length, segment length, segment area... etc.

Terminology related to circles in math:

Origin : It is a center(equidistant) point of the circle. Here “O” is the origin of the circle.

Radius : Distance from center of circle to any point around it circumference is called Radius of the circle. Generally it is denoted by ” r “.

Diameter: The longest distance from one end of a circle to the other end of the circle is called dia of the circle. Generally it is denoted by ” D ” . Diameter of the circle = 2 x Radius of the circle. i. e D = 2r.

Arc of a circle: It is a part of the circumference of the circle. The bigger one is called the major arc and the smaller one the minor arc.

Sector of a circle: It is a part of the area of a circle between two radii (a circle wedge).

Chord : A line segment within a circle that touches two points on the circle is called chord of a circle.

Circumference : The distance around the circle is called circumference or perimeter of the circle.

Pi ( π ): It is a number equal to 3.141592… or 22/7.

The pi ( π ) = (The circumference) / (The diameter) of any circle.

Tangent of circle: a line perpendicular to the radius that touches ONLY one point on the circle.

Secant of circle : A line that intersects a circle at two points then it is called Secant of circle.

Properties of circle :

Congruency: Two circles can be congruent if and only if they have equal radii.
The perpendicular from the center of a circle to a chord bisects the chord. The converse is also true.
The perpendicular bisectors of two chords of a circle intersect at its center.
There can be one and only one circle passing through three or more non -collinear points.
If two circles intersect in two points then the line through the centers is the perpendicular bisectors of the common chord.
If two chords of a circle are equal, then the center of the circle lies on the angle bisector of the two chords.
Equal chords of a circle or congruent circles are equidistant from the center.
Equidistant chords from the center of a circle are equal to each other in terms of their length.
The degree measure of an arc of a circle is twice the angle subtended by it at any point on the alternate segment of the circle.
Equal chords of a circle ( or of congruent circles) subtended equal angles at the center.(at the corresponding centers) The converse is also true.
If the sum of the opposite angles of a quadrilateral is 180°, then the quadrilateral is cyclic.
Secant means a line that intersects a circle at two points. Tangent means it is a line that touches a circle at exactly one point.
In two concentric circles , the chord of the larger circle that is tangent to the smaller circle is bisected at the point of contact.

Circle Formulas in Math :

Area and circumference of a circle:

Here Origin of the circle = O , Diameter = D and Radius = r

Area of a circle (A ) = π r ² =( π/4 ) D² = 0.7854 D²
Circumference of a circle ( C ) = 2 π r = π D.

Area of circle =( 1/2) x Circumference x radius

A = (1/2) x C x r

Diameter of a circle (D) = √(A/0.7854).

Arc and sector of a circle:

Here angle between two radii is ” θ” in degrees. . And sector of a circle AOB.
Arc length of circle( l ) (minor) = ( θ /360) x 2 π r = θ π r / 180

Area of the sector (minor) = ( θ /360) x π r ²

If the angle θ is in radians, then

The area of the sector = (θ/2) r ²

Sector angle of a circle θ = (180 x l )/ (π r ).