Finding the center of a circle or arc
Geometry construction using a compass and straightedge
This page shows how to find the center of a circle or arc with compass and straightedge or ruler.
This method relies on the fact that, for any
of a circle, the
of the chord always passes through the center of the circle. By applying this twice to two different chords, the center is established where the two bisectors intersect. A Euclidean construction
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.
The image below is the final drawing from the above animation.
||RS is a chord of the circle C
||A chord is a line segment linking two points on a circle.
See Chord definition.
||AC is the perpendicular bisector of the chord RS
||AC was drawn by constructing the perpendicular bisector of RS.
See Constructing the perpendicular bisector of a segment for the method and proof
||BC is the perpendicular bisector of the chord PQ
||As in (1) and (2)
||The center of the circle lies on the line AC.
||The perpendicular bisector of a chord passes through the center of the circle.
See Chord definition.
||The center of the circle lies on the line BC.
||As in (4).
||Point C is the center of the circle.
||The only point common to both AC and BC.
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.
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Other constructions pages on this site
Circles, Arcs and Ellipses
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