Five Tangent Circles

A circle of radius 1 is drawn in the plane. Four non-overlapping circles each of radius 1, are drawn (externally) tangential to the original circle. An angle \(\gamma\) is chosen uniformly at random in the interval \([0,2\pi)\). The probability that a half ray drawn from the centre of the original circle at an angle of \(\gamma\) intersects one of the other four circles can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

Details and assumptions

The half ray from the centre of the fifth circle at angle \(\gamma\) goes only in one direction, not both.

×

Problem Loading...

Note Loading...

Set Loading...