It
will be hard for students to locate the centers of the three circles.

Students
can discover the property in the solution by experimenting with
circles of different sizes.

This
property allows you to draw the circle that passes through points
E, D, and C. The other two circles are found
in the same way. By using this property, you can construct the
figure as it is described in the problem.

Solution

No
matter what triangle is chosen, and no matter what points are selected
on the sides of the triangle, the three circles intersect in a common
point, 0.

The
theorem is stated as follows: If a point is selected on each side
of a triangle, then the circles determined by each vertex and
the points on the sides that intersect at that vertex pass through
a common point.