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?