_{1}and C

_{2}touch at exactly one point.

Both circles also are tangent to a straight line L, at points Q

_{1}and Q

_{2}respectively.

The center of C

_{1}is P

_{1}, and the center of C

_{2}is P

_{2}.

The radius of C

_{1}is R and the radius of C

_{2}is r.

(i) Find the area of the trapezium T with vertices Q

_{1}P

_{1}P

_{2}Q

_{2}in terms of R and r

(ii) Given that R + r = 10 units, find the maximum area of T.