{"status": "success", "data": {"description_md": "In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\\triangle ABC$ is $50$ units and the area of $\\triangle ABC$ is $100$ square units?\n\n$\\textbf{(A) }0\\qquad\\textbf{(B) }2\\qquad\\textbf{(C) }4\\qquad\\textbf{(D) }8\\qquad\\textbf{(E) }\\text{infinitely many}$", "description_html": "<p>In a given plane, points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  are  <span class=\"katex--inline\">10</span>  units apart. How many points  <span class=\"katex--inline\">C</span>  are there in the plane such that the perimeter of  <span class=\"katex--inline\">\\triangle ABC</span>  is  <span class=\"katex--inline\">50</span>  units and the area of  <span class=\"katex--inline\">\\triangle ABC</span>  is  <span class=\"katex--inline\">100</span>  square units?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }0\\qquad\\textbf{(B) }2\\qquad\\textbf{(C) }4\\qquad\\textbf{(D) }8\\qquad\\textbf{(E) }\\text{infinitely many}</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": "2019 AMC 10B Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p11", "prev": "/problem/19_amc10B_p09"}}