This article popularly explains how to find the radius of a circle inscribed in a square. The theoretical material will help you understand all the nuances related to the topic. After reading this text, you can easily solve similar problems in the future.
Basic Theory
Before you go directly to finding the radius of a circle inscribed in a square, you should familiarize yourself with some fundamental concepts. Perhaps they may seem too simple and obvious, but they are necessary to understand the issue.
A square is a quadrilateral, all sides of which are equal to each other, and the degree measure of all angles is 90 degrees.
Circle is a two-dimensional closed curve located at a certain distance from some point. A segment, one end of which lies in the center of the circle, and the other end lies on any of its surfaces, is called a radius.
Familiarized with the terms, only the main question remains. We need to find the radius of a circle inscribed in a square. But what does the last sentence mean? Nothing here either.complex. If all sides of a certain polygon touch a curved line, then it is considered inscribed in this polygon.
Radius of a circle inscribed in a square
Theoretical material is over. Now we need to figure out how to put it into practice. Let's use a picture for this.
The radius is obviously perpendicular to AB. This means that at the same time it is parallel to AD and BC. Roughly speaking, you can "overlay" it on the side of the square to further determine the length. As you can see, it will correspond to the segment BK.
One of its ends r lies in the center of the circle, which is the intersection point of the diagonals. The latter, according to one of their properties, divide each other in half. Using the Pythagorean theorem, you can prove that they also divide the side of the figure into two identical parts.
Accepting these arguments, we conclude:
r=1/2 × a.
