mess with tangents

Question

I have reviewed and drawn this problem several times but I can not see the solution, it must be very simple but I do not see it Help me please

EDIT

Answer 1

Let mark the segments from $A$ with $y$ and from $C$ with $z$. Then we have:

$$ y+x+a =5$$ $$ y+a'+b+a'+z = 8$$ $$ x+a+b+z = 6$$

It is easy to see that $a=a'$: If we extend outer common tangents to say common point $T$ we see that $2a+b +t = 2a'+b+t $, so $a=a'$.

So $$5+6-8 = (y+x+a)+( x+a+b+z)- (y+a'+b+a'+z) = 2x$$