{"status": "success", "data": {"description_md": "Let $ABCDE$ be a pentagon inscribed in a circle such that $AB = CD = 3$, $BC = DE = 10$, and $AE= 14$.  The sum of the lengths of all diagonals of $ABCDE$ is equal to $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers.  What is $m+n$ ?\n\n$\\textbf{(A) }129\\qquad<br>\\textbf{(B) }247\\qquad<br>\\textbf{(C) }353\\qquad<br>\\textbf{(D) }391\\qquad<br>\\textbf{(E) }421\\qquad$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">ABCDE</span>  be a pentagon inscribed in a circle such that  <span class=\"katex--inline\">AB = CD = 3</span> ,  <span class=\"katex--inline\">BC = DE = 10</span> , and  <span class=\"katex--inline\">AE= 14</span> .  The sum of the lengths of all diagonals of  <span class=\"katex--inline\">ABCDE</span>  is equal to  <span class=\"katex--inline\">\\frac{m}{n}</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are relatively prime positive integers.  What is  <span class=\"katex--inline\">m+n</span>  ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }129\\qquad\\textbf{(B) }247\\qquad\\textbf{(C) }353\\qquad\\textbf{(D) }391\\qquad\\textbf{(E) }421\\qquad</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2014 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12B_p25", "prev": "/problem/14_amc12B_p23"}}