Captain America's Shield

Geometry Level 2

The front face of Captain America's shield (refer to this image drawn to scale) is made up of 4 circles and a 5-pointed regular star polygon which are all concentric. The 5-pointed star is tangential to the smallest circle at the 5 points seen in the figure. The diameters of the 4 circles are 30, 23, 18 and 12 inches respectively (yes, those are the real dimensions). Calculate the ratio \(\frac{\mbox{blue and red coloured area}}{\mbox{white area}}\).

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