# Incenter Exploration (B)

- Author:
- MsBuist, Tim Brzezinski

- Topic:
- Circle

**NCENTER**of the triangle. In the applet below,

**point I**is the triangle's

**INCENTER**. Use the tools of GeoGebra in the applet below to complete the activity below the applet.

*Be sure to answer each question fully as you proceed.*

**Directions:
**1) Click the checkbox that says "Drop Perpendicular Segments from I to sides.
2) Now, use the **Distance** tool to measure and display the lengths *IG*, *IH*, and *IJ*. What do you notice?

3) Experiment a bit by moving any one (or more) of the triangle's vertices around Does your initial observation in (2) still hold true? Why is this?

4) Construct a circle centered at I that passes through *G*. What else do you notice
Experiment by moving any one (or more) of the triangle's vertices around.
This circle is said to be the triangle's *incircle*, or *inscribed circle.
* It is the largest possible circle one can draw *inside* this triangle.
Why, according to your results from (2), is this possible?

5) Do the angle bisectors of a triangle's interior angles also bisect the sides opposite theses angles?
Use the **Distance** tool to help you answer this question.

6) Is it ever possible for a triangle's **INCENTER** to lie OUTSIDE the triangle
If so, under what condition(s) will this occur?

7) Is it ever possible for a triangle's **INCENTER** to lie ON the triangle itself?
If so, under what condition(s) will this occur?