This should be easy! Right? Part - 3

Geometry Level 5

The figure above represents two circles where \(AB=5\) units, \(\angle BAC=30^\circ\), \(\angle BMD=135^\circ\), \(MD = 3.3\) units and \(N\) is the mid point of \(MD\).

\[\dfrac{CD}{CN}\times{CM}=\frac{a\sqrt{c-\sqrt{d}+\sqrt{e}}}{b\sqrt{e}\sqrt{b-\sqrt{d}+\sqrt{e}}}\]

The equation above holds true for positive integers \(a,b,c,d\) and \(e\) with \(b,d\) and \(e\) square-free, \(a>b\), and \(a,b\) are coprime.

Find \(a+b+c+d+e\).

Clarification: \(MD\) a diameter of the smaller circle. \(M\) is the centre of the larger circle. The two circles tangential at \(D\).


Try Part-1 and Part-2 also.
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