Помогите решить 2 геометрических задачи

[незваный гость]

ins- писал(а):

It proves indeed very interesting result - there exists infinitely many triples of positive of numbers - that are solutions of the given equation with properties: a+b>c, b+c>a, c+a>b.

It does not prove. It proves only that if a triangle exists, its sides satisfy an equation. May be equivalence of that, but it does not matter: the existence of $a,b,c$ satisfying the equation is not proven.

[ins-]

I'm not sure but I think if we fix $ tg \frac{\alpha}{2} $ and have a success with finding $ tg \frac{\beta}{2} $ such that $ \alpha $ and $ \beta$ may be angles in some triangle our equation will have a solution. but take in mind that we express with sine law sides of this triangle - by angles and R - by varying R we will have infinitely many solutions of our equation.

[незваный гость]

There is a misunderstanding here. I think, first part proves everything. It is the second part that does not prove what you intend.

[ins-]

Goal of the second part is just to show explicit relation between the sides ot the triangle with required property.