Big turn

Geometry Level 5

In $$\triangle RED$$, $$\measuredangle DRE=75^{\circ}$$ and $$\measuredangle RED=45^{\circ}$$. $$|RD|=1$$. Let $$M$$ be the midpoint of segment $$\overline{RD}$$. Point $$C$$ lies on side $$\overline{ED}$$ such that $$\overline{RC}\perp\overline{EM}$$. Extend segment $$\overline{DE}$$ through $$E$$ to point $$A$$ such that $$CA=AR$$. Then $$AE=\frac{a-\sqrt{b}}{c}$$, where $$a$$ and $$c$$ are relatively prime positive integers, and $$b$$ is a positive integer. Find $$a+b+c$$.

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