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Stephani Eckelkamp

Internal Angle Bisectors: An Exploration

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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?

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