**Stephani Eckelkamp**

**Internal Angle
Bisectors: An Exploration**

**What picture is formed when
the angle bisectors of a triangle are extended to meet the circumcircle? **

** **

**Here is a picture, ****Δ****ABC is the original triangle,
and ****Δ****LMN is the triangle formed by
the angle bisectors crossing the circumcircle.**

****Both pictures are of the
same construction****

**Click here
to open this GSP sketch**

** **

**Here are some relationships
between these two triangles:**

**(Using the picture above and
to the right to make these calculations)**

** **

**Using the angles, we can see
these relationships:**

**Looking at the line segments
we can see these relationships**:

** **

**Manipulate the GSP sketch to
see if any ratios can be found for acute triangles only. Does the same hold true for other
classifications of triangles?**