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Table of Contents

**What is a Circle?**

A circle is simply a two-dimensional geometrical shape. A circle can be defined as any locus of points that are equidistant from a given point, called it’s center. It’s one of several possible shapes that arise from making marks on paper or another two-dimensional surface in such a way that each successive mark traces outlines connecting to earlier marks.

- The formula for a circle’s circumference is given by

C = 2πr,

where r is its radius.

- The distance around a circle’s circumference is called its perimeter, and it can be calculated using

p = 2πr or p = C/2,

where C is its circumference.

- Calculating the area of a circle can be done using

A = πr2 or A = C/π

- The diameter of a circle and the distance across it at its widest point can be calculated using d = 2r or d = 2C/π.

Parts of Circle

Different portions of a circle exist depending on their placements and qualities. The various sections of a circle are described in depth below.

**Annulus:**An annulus is defined as a ring-shaped figure. The area of an annulus can be calculated by subtracting the area of its inner circle from that of its outer circle.**Arc:**An arc is defined as any part of a circle that connects two points on its circumference.**Sector:**A sector is defined as any part of a circle that does not include its center.**Segment:**A segment is defined as any part of a circle, excluding its center and outermost edge.**Center:**The center of a circle is defined as its middle point.**Chord:**A chord is defined as any line segment that connects two points on a circle’s circumference.**Diameter:**A diameter is defined as any line segment that runs from one edge of a circle to its opposite side.**Radius:**A radius is defined as any line segment that connects a circle’s center to its outermost edge.**Secant:**A secant is defined as any line that intersects two or more circles.**Tangent:**A tangent is defined as any line that touches only one circle.

**Properties of Circle**

A circle has a number of important features, including the following:

- A circle’s outer line is equidistant from its center.
- The circle’s diameter divides it into two equal sections.
- A circle with one radius is congruent with another circle of the same radius.
- Comparing circles of varying sizes or of varying radii is also possible.
- Circles have a diameter that is double their radius, which is the chord with the greatest thickness.
- The smallest chord is a semicircle.
- The other chords are intermediate between these two extremes.
- If a chord intersects a circle, then it is called an arc of that circle.
- If a chord does not intersect a circle, then it is called an external or common chord of that circle.
- An angle inscribed in a semicircle is always right; an angle inscribed in any other kind of chord is obtuse if its measure exceeds 90° and acute if less than 90°.

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