Circles are two-dimensional shapes formed by a line rotating around a point, measured in radians. They can be represented on a graph through equations and are essential in solving mathematical problems. Let's dive into how to find the radius of a circle and explore its properties and theorems.

Circle Equations

There are two commonly used circle equations:

• Standard Circle Equation: This formula represents all circles with a center at (a, b) and a radius of r: (x-a)^2 + (y-b)^2 = r^2
• Circle at the Origin: When the center of a circle is at the origin, the equation becomes simpler without any constants attached to the x- or y-coordinate: x^2 + y^2 = r^2

Partitioning a Circle

Before delving into equations, it is important to understand how to divide a circle into parts, which is commonly used in solving problems related to circles. Arc: A section of the circle's circumference.

<