THE PROBLEM:

Let angle A of triangle ABC have measure 120 degrees.

Let A' be the point of intersection of segment BC and the angle
bisector of angle A.
Likewise B' is the intersection of AC and the angle bisector of angle
B, and C' is the intersection of AB and the angle bisector of angle C.

Prove angle B'A'C' is always a right angle.

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Construct a GSP animation to see the implementation as points B and C are moved away from or toward point A.

Click HERE for one implementation.

Construct a proof with descriptive (i.e. non-coordinate) geometry.

Construct a proof using coordinate geometry methods.