# Internal Triangle Area

Geometry Level 4

In triangle $$ABC$$, $$\angle A = 100^\circ, \angle B = 60^\circ$$ and $$BC$$ has side length 1. Let $$D$$ be the midpoint of side $$AC$$, and $$E$$ is a point on side $$BC$$ such that $$\angle EDC = 80^\circ$$. The value of $$[ABC] + 2 [CDE]$$ can be expressed as $$\frac { \sqrt{a}} {b}$$, where $$a$$ and $$b$$ are positive coprime integers. What is the value of $$a+b$$?

Note: $$[PQRS]$$ denotes the area of figure $$PQRS$$.

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