Variable circles $C_1,C_2,C_3,C_4$ with radii a,b,c,d respectively and centres above x-axis touch a fixed line y = 0 at the points P(–4,0), Q(4,0), R,S respectively. If circles $C_{1}and{C}_2$ touches each other externally at M and $C_3$ touches $C_1,C_{2}and{C}_4$ externally, also given that $C_4$ is externally tangent to $C_1$ On the basis of above answer the following.