Given a triangle ABC, we need to construct the circumcircle, and we need to construct the internal angle bisectors of triangle ABC and extend them to meet the circumcircle at points L, M, and N, respectively.
Now we need to construct the triangle LMN, and find a relationship between the measures of angles L, M, and N and the measures of angles A, B, and C.
Click here to explore the angle measures using GSP.
After exploring the angles measures, we find the following relationships:
Click here to verify this relationship using GSP.
Now it's time to prove this relationship! Click here for the proof.