# 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 \(a+b+c\).