the Nine Point Circle

Click on the sketch below to practice constructing a circle given three points on it. The instruction are below the picture.

In order to do this construction, we need to find the center of the circle. It is a geometric fact that the perpendicular bisector of a chord of a circle passes through the center. Since a chord is just a line segment with endpoints on a circle, any line segments we make with our three points will be chords on our yet undiscovered circle. So we can use the following strategy...

- Draw two different chords using the three given points.
- Construct the perpendicular bisector of each chord. They will intersect in the center of the circle.
- Now construct a circle using this center and one of your three points as a radius point.

If you have done your construction correctly, you will have a circle through all three points.

This construction is very similar to the construction you did to find the circumcenter. If you want to explore the circumcenter further, you can link to the Main Menu and look at the Triangle Investigation about the perpendicular bisectors of the sides of a triangle.

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