WSP Circumcircle

• ## Circumcircle

This applet allows for the construction and exploration of a circumcircle.
This interactive is optimized for your desktop and tablet.

### How to Use

• Use the red points to adjust the distances between the three points.

### Buttons

The buttons are meant to be used sequentially.

• Steps- By clicking on these buttons, you will reveal the next step in the construction.
• Show Measurements- will reveal the distance of each point to the circumcenter.
• At any time, you can press the Reset button to start over.

### Exploration

Before using any of the buttons, explore the following:

This interactive shows the location of three cities in relation to one another. Where should a major hospital be built so that it is equidistant to each city?

At any time, answer the following questions:

• When does the circumcenter lie outside of the triangle?
• Why are only two perpendicular bisectors needed to find the circumcenter?
• Why does this construction work? Create a formal proof.

### Objectives and Standards

NCTM Standards and Expectations
• Geometry / Measurement
• Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
• High School (9-12)
• Geometry
• Measurement