Question: Three circles with centers respectively $A,B,C$ are mutualy tangent. Express the radius of circle with center A in terms of BC, AC, and AB respectively.
My work: Let circles A, B, and C have radii a, b, and c, respectively and let $AB=x, AC=y, BC=z$. From here, I am not sure what to do. I tried systems of equations, but it didn't work.
Could someone please tell me what to do from here so that I can get the radius of circle A (a) and the reason behind it. I understand that there is a guess and check method to get the correct answer. However, it would be more helpful if someone could explain the rest of the algebra that I have to do to get to the answer.