Internal Triangle Area

Geometry Level 5

In triangle ABCABC, A=100,B=60 \angle A = 100^\circ, \angle B = 60^\circ and BCBC has side length 1. Let DD be the midpoint of side ACAC, and EE is a point on side BCBC such that EDC=80 \angle EDC = 80^\circ. The value of [ABC]+2[CDE] [ABC] + 2 [CDE] can be expressed as ab \frac { \sqrt{a}} {b}, where aa and bb are positive coprime integers. What is the value of a+ba+b?

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

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