 # Given a Segment, Construct Its Perpendicular Bisector; Given a Triangle, Construct Its Circumcircle

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This Demonstration shows two constructions:

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1. The perpendicular bisector of a segment .

2. The circumcircle of a triangle .

The second construction uses the first construction twice.

Construct the perpendicular bisector of and of . The center of the circumcircle of the triangle is the intersection of these bisectors.

Perpendicular Bisector

1. Draw the line segment .

2. Draw two circles with the same radius and centers and . (Any radius works as long as the circles intersect at two points.)

3. The circles intersect at two points, and . The perpendicular bisector of is the line through these two points. The point is the midpoint of .

Circumcircle

1. Draw a triangle .

2. Draw two perpendicular bisectors of —for example, of and . Let be the intersection of the two bisectors.

3. The circumcircle has center and radius .

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Contributed by: Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Euclid I. 10. Construct the midpoint of a given segment.

Euclid IV. 5. About a given triangle, circumscribe a circle.

Reference

 G. E. Martin, Geometric Constructions, New York: Springer, 1998, pp. 4–5.

## Permanent Citation

Izidor Hafner

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