Finding the center of a circle (with any right-angled object)

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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.

Note: This is not a Euclidean construction as defined in Constructions - Tools and Rules but a practical way to find the center of a circle when mathematical precision is not so important.

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

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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.

Step-by-step Instructions

Step 1	Place the right-angle corner of any object at any point on the circle. Any point will do.
Step 2	Make a mark where the two sides of the right-angle cross the circle.
Step 3	Draw a line between these two marks. Because of Thales Theorem, this is a diameter of the circle.
Step 4	Place the right-angle corner of the object at any other point on the circle. Any point will do, but for greatest accuracy, make it about a quarter the way round the circle from the first point.
Step 5	Make a mark where the two sides of the right-angle cross the circle.
Step 6	Connect these two points with a straight line. This is the second diameter.
Step 7	Done. The point where the two diameters intersect is the center of the circle.

Other constructions

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions