{"status": "success", "data": {"description_md": "In triangle $ABC,$ it is given that angles $B$ and $C$ are congruent. Points $P$ and $Q$ lie on $\\overline{AC}$ and $\\overline{AB},$ respectively, so that $AP=PQ=QB=BC.$ Angle $ACB$ is $r$ times as large as angle $APQ,$ where $r$ is a positive real number. Find the greatest integer that does not exceed $1000r.$\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 triangle <span class=\"katex--inline\">ABC,</span> it is given that angles <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span> are congruent. Points <span class=\"katex--inline\">P</span> and <span class=\"katex--inline\">Q</span> lie on <span class=\"katex--inline\">\\overline{AC}</span> and <span class=\"katex--inline\">\\overline{AB},</span> respectively, so that <span class=\"katex--inline\">AP=PQ=QB=BC.</span> Angle <span class=\"katex--inline\">ACB</span> is <span class=\"katex--inline\">r</span> times as large as angle <span class=\"katex--inline\">APQ,</span> where <span class=\"katex--inline\">r</span> is a positive real number. Find the greatest integer that does not exceed <span class=\"katex--inline\">1000r.</span></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": "2000 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_I_p15", "prev": "/problem/00_aime_I_p13"}}