Circumcenter - 2019

Topic:
Geometry

Follow the steps below to construct the circumcenter.

Use Toolbar Image to construct the perpendicular bisector of segments AB, BC and AC. Use Toolbar Image to add a point where the three perpendicular bisectors intersect. Use Toolbar Image to label the point where the perpendicular bisectors intersect.

The point where all three perpendicular bisectors intersect is called the circumcenter. 1. Use Toolbar Image to move point A, B or C so that the circumcenter is outside the triangle. What do you notice about the triangle?

Check all that apply

2. Use Toolbar Image to move point C so that the circumcenter lies on a side of the triangle. What do you notice about the triangle?

Check all that apply

We are now going to learn about the properties of a circumcenter.

Use Toolbar Image to draw a segment from A to the circumcenter. Use Toolbar Image to measure the length of the segment from A to the circumcenter. Repeat the process for vertex B and C Use Toolbar Image to draw a circle with center at the circumcenter and through point A.

Circumcenter Properties

3. Use Toolbar Imageto move point A, B or C around. What do you notice about the dashed segment lengths?

The Circle

4. You constructed the circle to go through point A. When you move the triangle, you should notice that the circle also always goes through B and C. Why is that?

Application for Circumcenter

5. For which of the following situations, would it make sense to find the circumcenter?

Check all that apply