{"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$\\textbf{(A) } 4 \\qquad\\textbf{(B) } 3\\sqrt{3} \\qquad\\textbf{(C) } 6 \\qquad\\textbf{(D) } 4\\sqrt{3} \\qquad\\textbf{(E) } 9$", "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, 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}, \\overline{BC},</span>  and  <span class=\"katex--inline\">\\overline{CA},</span>  respectively. Given that  <span class=\"katex--inline\">PQ=1, PR=2,</span>  and  <span class=\"katex--inline\">PS=3,</span>  what is  <span class=\"katex--inline\">AB?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 4 \\qquad\\textbf{(B) } 3\\sqrt{3} \\qquad\\textbf{(C) } 6 \\qquad\\textbf{(D) } 4\\sqrt{3} \\qquad\\textbf{(E) } 9</span> </p>\n<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 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10B_p18", "prev": "/problem/07_amc10B_p16"}}