Number of rotations

Geometry Level 3

Let \(f (x)\) be the relation from \(N->\){\(5,10\)} equal to \(10^{\circ}\) when \(x\) is odd and \(5^{\circ}\) when \(x\) is even. Here \(x\) denotes \(x^\text{th}\) rotation of point \((2,5)\) and \(f (x)\) is angle rotated clockwise by this \(x^\text{th}\) rotation when rotated about the point \((8,15)\). If after \(a\) rotations, the final point is again \((2,5)\), find the minimum value of \(\frac {a}{2}\).

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