{"status": "success", "data": {"description_md": "Isosceles trapezoid $ABCD$ has parallel sides $\\overline{AD}$ and $\\overline{BC},$ with $BC < AD$ and $AB = CD.$ There is a point $P$ in the plane such that $PA=1, PB=2, PC=3,$ and $PD=4.$ What is $\\tfrac{BC}{AD}?$\n\n$\\textbf{(A) }\\frac{1}{4}\\qquad\\textbf{(B) }\\frac{1}{3}\\qquad\\textbf{(C) }\\frac{1}{2}\\qquad\\textbf{(D) }\\frac{2}{3}\\qquad\\textbf{(E) }\\frac{3}{4}$", "description_html": "<p>Isosceles trapezoid  <span class=\"katex--inline\">ABCD</span>  has parallel sides  <span class=\"katex--inline\">\\overline{AD}</span>  and  <span class=\"katex--inline\">\\overline{BC},</span>  with  <span class=\"katex--inline\">BC &lt; AD</span>  and  <span class=\"katex--inline\">AB = CD.</span>  There is a point  <span class=\"katex--inline\">P</span>  in the plane such that  <span class=\"katex--inline\">PA=1, PB=2, PC=3,</span>  and  <span class=\"katex--inline\">PD=4.</span>  What is  <span class=\"katex--inline\">\\tfrac{BC}{AD}?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }\\frac{1}{4}\\qquad\\textbf{(B) }\\frac{1}{3}\\qquad\\textbf{(C) }\\frac{1}{2}\\qquad\\textbf{(D) }\\frac{2}{3}\\qquad\\textbf{(E) }\\frac{3}{4}</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": 4, "problem_name": "2022 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p24", "prev": "/problem/22_amc10A_p22"}}