1. ## Hyperbolic geometry

If a hyperbolic triangle has three equal angles, are its sides necessarily equal to each other?

Edit: Okay, so I have an idea that for any hyperbolic triangle ABC with sides a, b, and c, the following equalities hold:

$\frac{\sin A}{\sinh a} =\frac{\sin B}{\sinh b} = \frac{\sin C}{\sinh c}$

So if the angles are equal we have $\sinh a = \sinh b = \sinh c$ but I am not sure if this makes $a=b=c$.

2. ## Hyperbolic triangles and inscribed circles

Double post, sorry.