{"status": "success", "data": {"description_md": "Three of the edges of a cube are $\\overline{AB}, \\overline{BC},$ and $\\overline{CD},$ and $\\overline{AD}$ is an interior diagonal. Points $P, Q,$ and $R$ are on $\\overline{AB}, \\overline{BC},$ and $\\overline{CD},$ respectively, so that $AP=5, PB=15, BQ=15,$ and $CR=10.$ What is the area of the polygon that is the intersection of plane $PQR$ and the cube?\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>Three of the edges of a cube are <span class=\"katex--inline\">\\overline{AB}, \\overline{BC},</span> and <span class=\"katex--inline\">\\overline{CD},</span> and <span class=\"katex--inline\">\\overline{AD}</span> is an interior diagonal. Points <span class=\"katex--inline\">P, Q,</span> and <span class=\"katex--inline\">R</span> are on <span class=\"katex--inline\">\\overline{AB}, \\overline{BC},</span> and <span class=\"katex--inline\">\\overline{CD},</span> respectively, so that <span class=\"katex--inline\">AP=5, PB=15, BQ=15,</span> and <span class=\"katex--inline\">CR=10.</span> What is the area of the polygon that is the intersection of plane <span class=\"katex--inline\">PQR</span> and the cube?</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": 5, "problem_name": "1998 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/98_aime_p12", "prev": "/problem/98_aime_p10"}}