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

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

This Demonstration shows two constructions:

1. The perpendicular bisector of a segment .

AB

2. The circumcircle of a triangle .

ABC

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.

AC

BC

Perpendicular Bisector

1. Draw the line segment .

AB

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

AB

A

B

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 .

D

E

AB

F

AB

Circumcircle

1. Draw a triangle .

ABC

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

ABC

AC

BC

S

3. The circumcircle has center and radius .

S

AS