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Finding the center of a circle
Click here for a printable center-finding worksheet
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.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
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
(C) 2007 Copyright John Page
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