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

Geometry construction with compass and straightedge or ruler or ruler 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.

Constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions