{"status": "success", "data": {"description_md": "Point $P$ is inside equilateral $\\triangle ABC$. Points $Q$, $R$, and $S$ are the feet of the perpendiculars from $P$ to $\\overline{AB}$, $\\overline{BC}$, and $\\overline{CA}$, respectively. Given that $PQ=1$, $PR=2$, and $PS=3$, what is $AB$?\n\n$\\mathrm {(A)} 4\\qquad \\mathrm {(B)} 3\\sqrt{3}\\qquad \\mathrm {(C)} 6\\qquad \\mathrm {(D)} 4\\sqrt{3}\\qquad \\mathrm {(E)} 9$\n___\nFull 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>Point  <span class=\"katex--inline\">P</span>  is inside equilateral  <span class=\"katex--inline\">\\triangle ABC</span> . Points  <span class=\"katex--inline\">Q</span> ,  <span class=\"katex--inline\">R</span> , and  <span class=\"katex--inline\">S</span>  are the feet of the perpendiculars from  <span class=\"katex--inline\">P</span>  to  <span class=\"katex--inline\">\\overline{AB}</span> ,  <span class=\"katex--inline\">\\overline{BC}</span> , and  <span class=\"katex--inline\">\\overline{CA}</span> , respectively. Given that  <span class=\"katex--inline\">PQ=1</span> ,  <span class=\"katex--inline\">PR=2</span> , and  <span class=\"katex--inline\">PS=3</span> , what is  <span class=\"katex--inline\">AB</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} 4\\qquad \\mathrm {(B)} 3\\sqrt{3}\\qquad \\mathrm {(C)} 6\\qquad \\mathrm {(D)} 4\\sqrt{3}\\qquad \\mathrm {(E)} 9</span> </p>&#10;<hr><p>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": 3, "problem_name": "2007 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p15", "prev": "/problem/07_amc12B_p13"}}