Change bisector from one triangle to another

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SUMMARY

The discussion centers on the geometric relationship between the angle bisector LB of triangle ABC and the angle bisector AD of triangle AED. Participants explore the maximum possible value of the angle alpha formed between these two bisectors. The inquiry emphasizes the positioning of the triangles in the plane, suggesting that the configuration significantly influences the angle's measurement. A request for a visual sketch indicates the complexity of the geometric arrangement being analyzed.

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roni1
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LB is bisector of triangle ABC.
suppose, there is a new triangle that called AED.
alpha is a angle between LB to AD that is bisector of AED.
The triangles can be on any place in the plane.
What the value biggest angle ($$alpha$$) can be?
 
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roni said:
LB is bisector of triangle ABC.
suppose, there is a new triangle that called AED.
alpha is a angle between LB to AD that is bisector of AED.
The triangles can be on any place in the plane.
What the value biggest angle ($$alpha$$) can be?

This description lacks clarity ... can you upload a sketch to better understand what you mean?
 

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