ok.. here we go...
let's say the dist YZ is x cm, then the diameter of the larger circle is (10+x) cm. And the area is pi [(10+x)/2]^2. Similarly, the area of the smaller circle can be found ie pi(x/2)^2. We can then find an expression for the shaded area and equate that to the area of the smaller circle. You should get a wuadratic equation which can be reduced to
x^2 - 20x -100 = 0.
Solving this would give you the answer as required.
As for the second question, I think you should work on it alonmg similar lines as per question 1.
Hope it helps. Let me know if u need further clarifications.