Dart-throwing Monkeys

Geometry Level 2

A circular dart board has a radius of 9cm, the board is split into 3 regions. The first region is enclosed in a circle centered in the center of the dart board with a radius of 2cm. The second region is in between the circle that defines the first region and another circle also centered at the center of the dart board and with a radius of \(x\)cm. The third region is the rest of the dart board that is not occupied by the first or second region.

Monica the Monkey throws a dart at the dartboard. The Probability that the dart hits the second Region is \(\frac 59\). Find the value of \(x\).

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