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, ΔABC is the original triangle, and ΔLMN 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?