{"status": "success", "data": {"description_md": "In the adjoining figure, two circles of radii 6 and 8 are drawn with their centers 12 units apart. At $P$, one of the points of intersection, a line is drawn in such a way that the chords $QP$ and $PR$ have equal length. Find the square of the length of $QP$.<br><br>$\\includegraphics[width=166, height=104, totalheight=104]{https://latex.artofproblemsolving.com/7/6/b/76b9cef267eee686068f1d519a2f0cc0481e1160.png}$\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>In the adjoining figure, two circles of radii 6 and 8 are drawn with their centers 12 units apart. At <span class=\"katex--inline\">P</span>, one of the points of intersection, a line is drawn in such a way that the chords <span class=\"katex--inline\">QP</span> and <span class=\"katex--inline\">PR</span> have equal length. Find the square of the length of <span class=\"katex--inline\">QP</span>.<br/><br/><img src=\"https://latex.artofproblemsolving.com/7/6/b/76b9cef267eee686068f1d519a2f0cc0481e1160.png\" width=\"166\" height=\"104\" 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 14", "can_next": true, "can_prev": true, "nxt": "/problem/83_aime_p15", "prev": "/problem/83_aime_p13"}}