# 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 $$D$$.

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