What is a Circle?
The circle is one of the most common shapes in the world of geometry but have you ever thought what is a circle? A circle is defined as a set of points whose distances from a specific point are equal to each other. That specific point is known as the center of a circle and the distances are called the radius. This means that if we took any point of a circle and compare the distance with other point's distance, they will be equal. If this condition is void then we won't call it a circle. In other books, you might find this definition written in a different way but the meaning is the same. The other definition of a circle is the locus of points on the plane that are equidistant from a fixed point called the center. Circles have a specific equation, below is the graph of a circle:
The point C is the center of the circle and P is just a random point on the circumference. The distance from C to P is called the radius. You can take any other point beside P on the circle and you will find that the distance from the center is equal. To calculate the radius on the above graph, you need to use the distance formula.
and are the values on the ordinate,
and and are the values on the abscissa.
Through distance formula, you can find the value of radius. Since we are talking about circles, we will insert the above graph's data in this formula.
Since we are finding radius that is why we equated the right-hand side expression to the radius (which is denoted by "r"). We plugged the values of abscissa and ordinate in the equation. Now taking square on both sides to eliminate the root, it will now look like:
The above equation is the standard equation of a circle. This means that every circle's equation will be generated by the above formula.