## Introduction to the Basic Concepts of Circles

The Civil Service Exams also contain geometry problems, and so far, our discussions are mostly algebra problems. In this new series of posts, we will discuss how to solve geometry and measurement problems particularly about circles. However, before we start solving problems, let us first discuss the basic terminologies about circles.

A circle is a set of points equidistant to a point called the center of the circle. As I go around to give trainings and lectures , I usually hear the wrong definition below. I am not sure where this definition originated, but this is wrong.

Wrong Definition: A circle is a polygon with infinite number of sides.

If you look at the definition of a polygon (see Wikipedia), it is a region bounded with a finite number of straight lines (sides). So, if you say that a circle is a polygon with infinite number of sides, it is already a contradiction. Therefore, remember from now on that a circle is NOT a polygon and it has no side.

Parts of a Circle

Below is a circle with center O. A circle is usually named using its center, so we can call it circle O.

A segment from the center of a circle to a point on the circle such as $\overline{OC}$ is called radius (plural is radii, pronounced as raid-yay). A segment joining two points on the circle such as $\overline{DE}$ is called chord. The longest chord that can be made in a circle passes through the center. This chord is called diameter. In the figure above, $\overline{AB}$ is a diameter of circle O.

Notice that diameter $\overline{AB}$ is composed of two radii, $\overline{OA}$ and $\overline {OB}$. Therefore, the diameter of a circle is twice its radius. So, if we let the diameter D, and radius r, we can say that $D = 2r$.

If we measure the length of the circle, that is if we start from B, go around along the circle until we reach B again, the distance we would have traveled is called its circumference.  The formula circumference is $C = 2 \pi r$

where $\pi$ is approximately 3.1416.

Since $2 \pi r = \pi (2r)$ and $D = 2r$, we can also say that $C = \pi D$. Note that the circle itself (the path itself from B going around back to B) is also called circumference.

In this series, we will also learn how to calculate the area A of a circle in this series which has formula $A = \pi r^2$.

In the next post, we are going to discuss how to calculate the circumference of a circle.