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Incenter-Incircle

Grade:
9-12
Standards:
Geometry
Math Content:
Geometry

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

 
Release: 2015Q2, Semantic Version: 4.2.0, Build Number: 911.6-r, Build Stamp: dn.kcptech.com/20150706050244

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.

 

  • 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?