# Can't use Thales' theorem!

Geometry Level 4

Let a circle with radius 1 have centre $$O$$, and let $$AB$$ be its diameter. $$C$$, $$D$$ and $$E$$ are collinear points in that order such that $$C$$ is on $$AB$$ extended closer to $$A$$, $$D$$ and $$E$$ are on the circle and $$BE=ED=DC$$. If the value of $$\cos \angle EOB$$ can be represented as $$\dfrac {a}{b}$$, where $$a$$ is an integer, $$b$$ is a positive integer and both are coprime, find the value of $$a+b$$.

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