# Incenter Exploration (B)

- Author:
- Tim Brzezinski

Recall that 3 or more lines are said to be concurrent if and only if they intersect at exactly one point.
The angle bisectors of a triangle's 3 interior angles are all concurrent.
Their point of concurrency is called the I

**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? (If you need a hint, refer back to the worksheet found here. 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?