Let's first use a circular object such as a can or a saucer to draw a circle.
To construct the center of the circle, we will draw two chords of the circle.
Next, we need to construct the perpendicular bisectors of the chords. To start, we should put the compass point on point M and draw an arc. The opening of the compass must be greater than 12MN — it must go further than the midpoint between M and N. Otherwise, the arcs we draw will not intersect.
With the same compass setting, we will put the compass point on point N and draw another arc.
By drawing a line through the points of intersection we will get a perpendicular bisector of the segment MN. Let's label its points of intersection with the circle as A and B.
Similarly, we will draw a perpendicular bisector of the second chord KL.
Finally, let's recall what Theorem 12-10 states.
Theorem 12-10
In a circle, the perpendicular bisector of a chord contains the center of the circle.
According to the theorem, perpendicular bisectors AB and CD both contain the center of the circle. It is possible only if the center is their point of intersection.
