# JEE 2016! (will vectors help?)

Geometry Level 4

The Pentagon $$ABCDE$$ has the properties $$AB || CD , ED || BC , \dfrac{AB}{CD} = \dfrac12 , \dfrac{ED}{BC} = \dfrac13$$.

Given that the straight lines $$AD$$ and $$CE$$ intersect at point $$O$$ to form the ratios $$\dfrac{OC}{EO} = \dfrac ab$$ and $$\dfrac{OD}{AO} = \dfrac cd$$, where $$a,b,c,d$$ are positive integers with $$\gcd(a,b) = \gcd(c,d) = 1$$.

Find the value of $$a+b+c+d$$.

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