# Finding the center of a circle using any right-angled object

An easy way to find the center of a circle using any right-angled object. Here we use a 45-45-90 drafting triangle, but anything that has a 90° corner will do, such as the corner of a sheet of paper.

Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.

This page shows how to find the center of a circle using any right-angled object. This method works as a result of using Thales Theorem in reverse. The diameter of a circle subtends a right angle to any point on the circle. By placing the 90° corner of an object on the circle, we can find a diameter. By finding two diameters we establish the center where they intersect.

## Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

## Why it works

This method works as a result of Thales Theorem. The diameter of a circle subtends a right angle to any point on the circle. The converse is also true: A right angle on the circle must cut off a diameter. By finding two diameters, we find the center where they intersect.

Visit Thales Theorem for an animated description of how this works.