Finding the center of a circle
This demonstration shows how to find the center of a circle using only a compass and straightedge. See "Introduction to Euclidean Constructions" We start with a circle and establish a point C at the center of the circle.
(See also Finding the center of a circle using any right-angled object for a more practical, non-Euclidean, method)
NOTE: It assumes that you are familiar with the method of constructing a perpendicular bisector of a line segment. See Constructing a perpendicular bisector of a line segment
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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Step-by-step Instructions
Step 1 Using a straightedge, draw any two chords of the circle. For greatest accuracy, avoid chords that are nearly parallel.
Step 2 Construct the perpendicular bisector of one of the chords using the method described in Constructing a perpendicular bisector of a line segment
Step 3 Repeat for the other chord
Step 4 The point where the two lines intersect is the center C of the circle.
Explanation
The method relies on the fact that, for any chord of a circle, the perpendicular bisector of the chord always passes through the center of the circle. (For more see Definition and Properties of a Chord)
By applying this fact twice to two different chords, the center is established where the two bisectors intersect.
Try it yourself
Click here for a printable worksheet containing two center-finding problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions