Circumcircle of a Triangle Construction

Explore the construction of the circumcircle of a triangle

If you are not familiar with the construction steps necessary for the construction of the circumcircle of a triangle, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.

Task

Construct a the circumcircle of a triangle that passes the Drag Test by following the construction steps provided below.

Try it yourself...

Construction steps

1.		Create an arbitrary triangle ABC.
2.		Construct the Perpendicular Bisector for each side of the triangle. Hint: The tool Perpendicular Bisector can be applied to an existing segment.
3.		Create intersection point D of two of the line bisectors. Hint: The tool Intersect can be applied to the intersection of three lines or by successively selecting two of the three line bisectors.
4.		Construct a circle with center D through one of the vertices of triangle ABC.
5.		Perform the Drag Test to check if your construction is correct.

Hint: You might want to save your construction using the

File menu.

Back to school...

Modify your construction to answer the following questions:

Can the circumcenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true?
Try to find an explanation for using line bisectors in order to create the circumcenter of a triangle.