Two externally tangent circles on a baseline

Core stretch

Two circles rest on the same horizontal line and touch externally. The larger centre is \(O\), radius \(15\) cm; the smaller centre is \(C\), radius \(x\) cm. The horizontal through \(O\) meets the vertical through \(C\) at \(B\), and \(B\) lies on the larger circle. Let vertical feet be \(E,F\).

You may use the facts that a radius to the point of contact with a straight line is perpendicular to the line, and that externally touching circles have centre separation equal to the sum of their radii.

1. Express
   1. \(OC\),[2]
   2. \(BC\), in terms of \(x\).[2]
2. Find \(x\).[2]
3. Find area of trapezium \(OCFE\).[2]