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Problem of the Week
Problem D
Coloured Areas

Chandra wishes to paint a sign. The sign is composed of three concentric semi-circles, creating an outer band, a middle band, and an inner semi-circle.

The top edge of the sign is the largest semi-circle and the bottom edge is a diameter of this semi-circle. A medium semi-circle and a small semi-circle are also drawn with diameters centred along the bottom edge. The outer band is the region between the largest semi-circle and the medium semi-circle. The middle band is the region between the medium semi-circle and the small semi-circle.

The outer band is divided into five regions of equal area and will be painted blue. Each of these regions is labelled with a \(B\). The middle band is divided into three regions of equal area and will be painted red. Each of these regions is labelled with an \(R\). The inner semi-circle will be painted white.

The diameter of the largest semi-circle is \(10\) m and the diameter of the middle semi-circle is \(6\) m.

If the ratio of the area of one region marked with an \(R\) to the area of one region marked with a \(B\) is \(5:6\), what is the diameter of the inner semi-circle?