2 Blue Moons

Geometry Level 5

4 circles are situated between 2 parallel lines and tangent to each other and to the lines as per diagram. The radii of \(C_1\) and \(C_2\) are 18 and 6 respectively..

If \(x\) is the radius of \(C_3\) and \(y\) is the radius of \(C_4\), find \(x + y\) to the nearest 3 decimal places.

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