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