**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.

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 using coordinate geometry methods.

Construct a proof with with geometry methods.