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A broken gear needs to be replaced, but only a piece of it is available. To order a replacement gear, the radius of the original must be found. Explain how to use the perpendicular bisectors of a triangle to find the radius of the original gear.

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Investigation 5-1: Constructing the Perpendicular Bisectors of the Sides of a Triangle

Tools Needed: paper, pencil, compass, ruler

1. Draw a scalene triangle.

2. Construct the perpendicular bisector (Investigation 1-3) for all three sides.

The three perpendicular bisectors all intersect at the same point, called the circumcenter.

Circumcenter: The point of concurrency for the perpendicular bisectors of the sides of a triangle.

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