Question # 1

Given three points in the plane, how can I locate the center
of the circle that has those three points on its
circumference?

Name the three points, A,B,C.
Conect each of the points to each other.
You have now drawn a triangle.
The sides of the triangle are the edges,
[A,B], [A,C], and [B,C].

Find the midpoints of each of the edges.
Let P be the midpoint of [A,B].
Let Q be the midpoint of [A,C].
Let R be the midpoint of [B,C].

At P, construct the line perpendicular to [A,B].
Give this perpendicular the name J.
All points on J are equal distant from A and B.

At Q, construct the line perpendicular to [A,C].
Give this perpendicular the name K.
All points on K are equal distant from A and C.

The point where J intersects K is equal distant from A,B and
C.

This is the point that is the center of the circle that has,
A,B and C on its circumference.

Confirm correctness by drawing the perpendicular to [B,C]
from R, the midpoint of [B,C]. That perpendicular bisector of
[B,C] should go through the center just found.

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