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

perpendicular bisector

circumcircle

A

B

C

steps

1

2

3

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

AC

and of

BC

. The center of the circumcircle of the triangle is the intersection of these bisectors.

Perpendicular Bisector

1. Draw the line segment

AB

.

2. Draw two circles with the same radius

AB

and centers

A

and

B

. (Any radius works as long as the circles intersect at two points.)

3. The circles intersect at two points,

D

and

E

. The perpendicular bisector of

AB

is the line through these two points. The point

F

is the midpoint of

AB

.

Circumcircle

1. Draw a triangle

ABC

.

2. Draw two perpendicular bisectors of

ABC

—for example, of

AC

and

BC

. Let

S

be the intersection of the two bisectors.

3. The circumcircle has center

S

and radius

AS

.