

Finding the center of a circle using any rightangled object
An easy way to find the center of a circle using any rightangled object. Here we use a 454590 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 rightangled 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 stepbystep instructions
The above animation is available as a
printable stepbystep 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.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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