# Thread: Find angles of triangle if AB+AD=CD and AC+AD=BC (very hard for me)

1. ## Find angles of triangle if AB+AD=CD and AC+AD=BC (very hard for me)

This question is much harder than it looks. I tried for a very long time but could not solve it.

Let AD be the angle bisector of angle A in triangle ABC. Given that AB+AD=CD and AC+AD=BC, find the angles of triangle ABC.

@below
Sorry I understand now. I tried a ton of law of cosines bashing and representing the lengths in terms of the sides of the triangle but I could not find a clean way to find the angles of the triangle.

2. Originally Posted by project math
This question is much harder than it looks. I tried for a very long time but could not solve it.

Let AD be the angle bisector of angle A in triangle ABC. Given that AB+AD=CD and AC+AD=BC, find the angles of triangle ABC.

What are your thoughts?

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