{"status": "success", "data": {"description_md": "In $\\triangle ABC$ with a right angle at $C,$ point $D$ lies in the interior of $\\overline{AB}$ and point $E$ lies in the interior of $\\overline{BC}$ so that $AC=CD,$ $DE=EB,$ and the ratio $AC:DE=4:3.$ What is the ratio $AD:DB?$\n\n$\\textbf{(A) } 2:3\n\\qquad\\textbf{(B) } 2:\\sqrt{5}\n\\qquad\\textbf{(C) } 1:1\n\\qquad\\textbf{(D) } 3:\\sqrt{5}\n\\qquad\\textbf{(E) } 3:2$", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle ABC</span>  with a right angle at  <span class=\"katex--inline\">C,</span>  point  <span class=\"katex--inline\">D</span>  lies in the interior of  <span class=\"katex--inline\">\\overline{AB}</span>  and point  <span class=\"katex--inline\">E</span>  lies in the interior of  <span class=\"katex--inline\">\\overline{BC}</span>  so that  <span class=\"katex--inline\">AC=CD,</span>   <span class=\"katex--inline\">DE=EB,</span>  and the ratio  <span class=\"katex--inline\">AC:DE=4:3.</span>  What is the ratio  <span class=\"katex--inline\">AD:DB?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2:3\n\\qquad\\textbf{(B) } 2:\\sqrt{5}\n\\qquad\\textbf{(C) } 1:1\n\\qquad\\textbf{(D) } 3:\\sqrt{5}\n\\qquad\\textbf{(E) } 3:2</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": "2019 AMC 10B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p17", "prev": "/problem/19_amc10B_p15"}}