Pythagorean relationship between the radii of a circular crown

Abstract

One of the most important theorems of mathematics, as it is a basic tool in solving geometric problems, is the Pythagorean theorem. Which states that in a right triangle the sum of the squares of its legs is equal to the square of its hypotenuse, so a specific geometric relationship is established for right triangles, however, more generally a Pythagorean relationship states that "The sum of the squares of two numbers A and B is equal to the square of a third C", therefore, this relationship can be found in various geometric contexts, such as in the case of two concentric circles (a circular crown), for this reason in this article the deduction of the existing Pythagorean relationship between the radii of a circular crown, as well as the three cases that can be realized in this situation. It also presents a geometric construction that can be obtained hard in the Pythagorean relationship of three circles and how different theorems can be deduced or applied from this.