Solving circle's radius only knowing angle & lengths of external triangle OR solving for sides of a triangle partial side lengths

Question

Is this possible?

Given that I know the length of Y and Z and the angle of X can I figure out the radius A?

If I can't without more information, I can produce another set of data X Y Z at a different angle x with an identical radius A.

How can I solve for radius A? And is there a method to solve side B without knowing radius A?

Answer 1

It is possible, indeed we have $$ (y+a)=(z+a)\cdot \cos(x) \iff a = \frac{y+z\cos(x)}{1-\cos(x)} $$