Circles are everywhere, and every circle can be described mathematically by either of two formulas. The first takes advantage of the Pythagorean Theorem. The second formula applies either the standard form or general form for the equation. We will look at both formulas.
When you consider a circle on a coordinate graph is the set of all points equidistant from a center point, you can see that those points can be described as an (x, y) value on the graph. Move right or left so many boxes (that's the x value), and then move up or down to the y value.
With the circle's center point also an (x, y) value, you can create a right triangle with the two sides x boxes left or right from that center point, and y boxes up or down from that same center point.
The radius, r, of the circle -- the distance from the center point to the circle itself -- now becomes the hypotenuse for every possible right triangle for every possible point.
A circle has infinite points, since points are dimensionless positions in space. So, at least in the pure science of mathematics, an infinite number of right triangles exist that satisfy a 2 + b 2 = c 2 ^+^=^ a 2 + b 2 = c 2 and every one of them has a vertex (of the hypotenuse and one side of the triangle) lying on the circle.
The Pythagorean Theorem shows a relationship between the two sides of a right triangle and its hypotenuse: a 2 + b 2 = c 2 ^+^=^ a 2 + b 2 = c 2