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.
Construct the circumcircle of a triangle that passes the Drag Test by following the construction steps provided below.
Try it yourself...
|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.|
|6.||Activate the Move tool and select point D. |
|7.||Start typing the new name |
|8.||Select OK to apply your changes and rename the point.|
Use 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 think of a real world application in which finding the circumcenter of a triangle would be useful.