{"status": "success", "data": {"description_md": "Let $ABCD$ be an isosceles trapezoid having parallel bases $\\overline{AB}$ and $\\overline{CD}$ with $AB>CD.$ Line segments from a point inside $ABCD$ to the vertices divide the trapezoid into four triangles whose areas are $2, 3, 4,$ and $5$ starting with the triangle with base $\\overline{CD}$ and moving clockwise as shown in the diagram below. What is the ratio $\\frac{AB}{CD}?$<br><center><img class=\"problem-image\" alt='[asy] unitsize(100); pair A=(-1, 0), B=(1, 0), C=(0.3, 0.9), D=(-0.3, 0.9), P=(0.2, 0.5), E=(0.1, 0.75), F=(0.4, 0.5), G=(0.15, 0.2), H=(-0.3, 0.5);  draw(A--B--C--D--cycle, black);  draw(A--P, black); draw(B--P, black); draw(C--P, black); draw(D--P, black); label(\"$A$\",A,(-1,0)); label(\"$B$\",B,(1,0)); label(\"$C$\",C,(1,-0)); label(\"$D$\",D,(-1,0)); label(\"$2$\",E,(0,0)); label(\"$3$\",F,(0,0)); label(\"$4$\",G,(0,0)); label(\"$5$\",H,(0,0)); dot(A^^B^^C^^D^^P); [/asy]' class=\"latexcenter\" height=\"172\" src=\"https://latex.artofproblemsolving.com/2/9/c/29c42141e2c79d3a16294b55a9be52158c6f9681.png\" width=\"382\"/></center>\n\n$\\textbf{(A)}\\: 3\\qquad\\textbf{(B)}\\: 2+\\sqrt{2}\\qquad\\textbf{(C)}\\: 1+\\sqrt{6}\\qquad\\textbf{(D)}\\: 2\\sqrt{3}\\qquad\\textbf{(E)}\\: 3\\sqrt{2}$\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>Let  <span class=\"katex--inline\">ABCD</span>  be an isosceles trapezoid having parallel bases  <span class=\"katex--inline\">\\overline{AB}</span>  and  <span class=\"katex--inline\">\\overline{CD}</span>  with  <span class=\"katex--inline\">AB&gt;CD.</span>  Line segments from a point inside  <span class=\"katex--inline\">ABCD</span>  to the vertices divide the trapezoid into four triangles whose areas are  <span class=\"katex--inline\">2, 3, 4,</span>  and  <span class=\"katex--inline\">5</span>  starting with the triangle with base  <span class=\"katex--inline\">\\overline{CD}</span>  and moving clockwise as shown in the diagram below. What is the ratio  <span class=\"katex--inline\">\\frac{AB}{CD}?</span> <br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(100); pair A=(-1, 0), B=(1, 0), C=(0.3, 0.9), D=(-0.3, 0.9), P=(0.2, 0.5), E=(0.1, 0.75), F=(0.4, 0.5), G=(0.15, 0.2), H=(-0.3, 0.5);  draw(A--B--C--D--cycle, black);  draw(A--P, black); draw(B--P, black); draw(C--P, black); draw(D--P, black); label(&#34;$A$&#34;,A,(-1,0)); label(&#34;$B$&#34;,B,(1,0)); label(&#34;$C$&#34;,C,(1,-0)); label(&#34;$D$&#34;,D,(-1,0)); label(&#34;$2$&#34;,E,(0,0)); label(&#34;$3$&#34;,F,(0,0)); label(&#34;$4$&#34;,G,(0,0)); label(&#34;$5$&#34;,H,(0,0)); dot(A^^B^^C^^D^^P); [/asy]\" height=\"172\" src=\"https://latex.artofproblemsolving.com/2/9/c/29c42141e2c79d3a16294b55a9be52158c6f9681.png\" width=\"382\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\: 3\\qquad\\textbf{(B)}\\: 2+\\sqrt{2}\\qquad\\textbf{(C)}\\: 1+\\sqrt{6}\\qquad\\textbf{(D)}\\: 2\\sqrt{3}\\qquad\\textbf{(E)}\\: 3\\sqrt{2}</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": "2021 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p18", "prev": "/problem/21_amc12B_p16"}}