 WSP Incenter-Incircle

• ## Incenter-Incircle

This applet allows for the discovery of the incenter and incircle of a triangle.

### Instructions

Upon opening the applet, three cities are shown (Helena, Salt Lake, and Boise). These three cities form a triangle.

### How to Use

You can change the shape of the triangle by dragging any one of the vertices.

### Buttons

• By clicking on the Find First Angle Bisector button (and any button that pops up afterwards), the next step in the construction will be revealed.
• At any time, you can press the Reset button to start over.

### Exploration

• What are the properties of the incenter?

• Can an incenter be located outside of the triangle? Why or why not?

• What are the properties of the incircle?

• How would you find the inradius?
• How about if the triangle were equilateral?

• Why does this construction work?
• Prove why the blue circle is indeed the incircle.

### Extension

How many points of concurrency does a triangle have?

### Objectives and Standards

NCTM Standards and Expectations
• Geometry / Measurement
• Functions and Trigonometry
• 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