{"status": "success", "data": {"description_md": "In $\\triangle ABC$, we have $AC = BC = 7$ and $AB = 2$. Suppose that $D$ is a point on line $AB$ such that $B$ lies between $A$ and $D$ and $CD = 8$. What is $BD$?\n\n$\\mathrm{(A)} 3 \\qquad \\mathrm{(B)} 2\\sqrt{3} \\qquad \\mathrm{(C)} 4 \\qquad \\mathrm{(D)} 5 \\qquad \\mathrm{(E)} 4\\sqrt{2}$", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle ABC</span> , we have  <span class=\"katex--inline\">AC = BC = 7</span>  and  <span class=\"katex--inline\">AB = 2</span> . Suppose that  <span class=\"katex--inline\">D</span>  is a point on line  <span class=\"katex--inline\">AB</span>  such that  <span class=\"katex--inline\">B</span>  lies between  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">CD = 8</span> . What is  <span class=\"katex--inline\">BD</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} 3 \\qquad \\mathrm{(B)} 2\\sqrt{3} \\qquad \\mathrm{(C)} 4 \\qquad \\mathrm{(D)} 5 \\qquad \\mathrm{(E)} 4\\sqrt{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": 1, "problem_name": "2005 AMC 10B Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10B_p11", "prev": "/problem/05_amc10B_p09"}}