{"status": "success", "data": {"description_md": "The adjoining figure shows two intersecting chords in a circle, with $B$ on minor arc $AD$. Suppose that the radius of the circle is 5, that $BC = 6$, and that $AD$ is bisected by $BC$. Suppose further that $AD$ is the only chord starting at $A$ which is bisected by $BC$. It follows that the sine of the minor arc $AB$ is a rational number. If this fraction is expressed as a fraction $m/n$ in lowest terms, what is the product $mn$?<br>$\\includegraphics[width=166, height=167, totalheight=167]{https://latex.artofproblemsolving.com/6/b/4/6b49bdb753edffad9ade586d305444d70beb3d80.png}$\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": "<p>The adjoining figure shows two intersecting chords in a circle, with <span class=\"katex--inline\">B</span> on minor arc <span class=\"katex--inline\">AD</span>. Suppose that the radius of the circle is 5, that <span class=\"katex--inline\">BC = 6</span>, and that <span class=\"katex--inline\">AD</span> is bisected by <span class=\"katex--inline\">BC</span>. Suppose further that <span class=\"katex--inline\">AD</span> is the only chord starting at <span class=\"katex--inline\">A</span> which is bisected by <span class=\"katex--inline\">BC</span>. It follows that the sine of the minor arc <span class=\"katex--inline\">AB</span> is a rational number. If this fraction is expressed as a fraction <span class=\"katex--inline\">m/n</span> in lowest terms, what is the product <span class=\"katex--inline\">mn</span>?<br/><img src=\"https://latex.artofproblemsolving.com/6/b/4/6b49bdb753edffad9ade586d305444d70beb3d80.png\" width=\"166\" height=\"167\" class=\"problem-image\"/></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 6, "problem_name": "1983 AIME Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/83_aime_p14"}}