{"status": "success", "data": {"description_md": "In $\\triangle RED, RD =1, \\angle DRE = 75^\\circ$ and $\\angle RED = 45^\\circ$. 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 $AE = \\tfrac{a-\\sqrt{b}}{c},$ where $a$ and $c$ are relatively prime positive integers, and $b$ is a positive integer. Find $a+b+c$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

In \\triangle RED, RD =1, \\angle DRE = 75^\\circ and \\angle RED = 45^\\circ. 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 = \\tfrac{a-\\sqrt{b}}{c}, where a and c are relatively prime positive integers, and b is a positive integer. Find a+b+c.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2014 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/14_aime_II_p12", "prev": "/problem/14_aime_II_p10"}}