{"status": "success", "data": {"description_md": "Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\\sqrt 2$, and $\\angle BAC = 45^\\circ$. Point $D$ is $20$ meters due north of point $C$. The distance $AD$ is between which two integers?\n\n$\\textbf{(A)}\\ 30\\ \\text{and}\\ 31 \\qquad\\textbf{(B)}\\ 31\\ \\text{and}\\ 32 \\qquad\\textbf{(C)}\\ 32\\ \\text{and}\\ 33 \\qquad\\textbf{(D)}\\ 33\\ \\text{and}\\ 34 \\qquad\\textbf{(E)}\\ 34\\ \\text{and}\\ 35$", "description_html": "<p>Point  <span class=\"katex--inline\">B</span>  is due east of point  <span class=\"katex--inline\">A</span> . Point  <span class=\"katex--inline\">C</span>  is due north of point  <span class=\"katex--inline\">B</span> . The distance between points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">C</span>  is  <span class=\"katex--inline\">10\\sqrt 2</span> , and  <span class=\"katex--inline\">\\angle BAC = 45^\\circ</span> . Point  <span class=\"katex--inline\">D</span>  is  <span class=\"katex--inline\">20</span>  meters due north of point  <span class=\"katex--inline\">C</span> . The distance  <span class=\"katex--inline\">AD</span>  is between which two integers?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 30\\ \\text{and}\\ 31 \\qquad\\textbf{(B)}\\ 31\\ \\text{and}\\ 32 \\qquad\\textbf{(C)}\\ 32\\ \\text{and}\\ 33 \\qquad\\textbf{(D)}\\ 33\\ \\text{and}\\ 34 \\qquad\\textbf{(E)}\\ 34\\ \\text{and}\\ 35</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": "2012 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc10B_p13", "prev": "/problem/12_amc10B_p11"}}