{"status": "success", "data": {"description_md": "Square $ABCD$ has center $O$, $AB=900$, $E$ and $F$ are on $AB$ with $AE<BF$ and $E$ between $A$ and $F$, $m\\angle EOF =45^\\circ$, and $EF=400$. Given that $BF=p+q\\sqrt{r}$, wherer $p,q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p+q+r$.\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>Square <span class=\"katex--inline\">ABCD</span> has center <span class=\"katex--inline\">O</span>, <span class=\"katex--inline\">AB=900</span>, <span class=\"katex--inline\">E</span> and <span class=\"katex--inline\">F</span> are on <span class=\"katex--inline\">AB</span> with <span class=\"katex--inline\">AE&lt;BF</span> and <span class=\"katex--inline\">E</span> between <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">F</span>, <span class=\"katex--inline\">m\\angle EOF =45^\\circ</span>, and <span class=\"katex--inline\">EF=400</span>. Given that <span class=\"katex--inline\">BF=p+q\\sqrt{r}</span>, wherer <span class=\"katex--inline\">p,q,</span> and <span class=\"katex--inline\">r</span> are positive integers and <span class=\"katex--inline\">r</span> is not divisible by the square of any prime, find <span class=\"katex--inline\">p+q+r</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": 5, "problem_name": "2005 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p13", "prev": "/problem/05_aime_II_p11"}}