{"status": "success", "data": {"description_md": "The interior of a quadrilateral is bounded by the graphs of $(x+ay)^2 = 4a^2$ and $(ax-y)^2 = a^2$, where $a$ is a positive real number. What is the area of this region in terms of $a$, valid for all $a > 0$?\n\n$\\textbf{(A)} ~\\frac{8a^2}{(a+1)^2}\\qquad\\textbf{(B)} ~\\frac{4a}{a+1}\\qquad\\textbf{(C)} ~\\frac{8a}{a+1}\\qquad\\textbf{(D)} ~\\frac{8a^2}{a^2+1}\\qquad\\textbf{(E)} ~\\frac{8a}{a^2+1}$", "description_html": "<p>The interior of a quadrilateral is bounded by the graphs of  <span class=\"katex--inline\">(x+ay)^2 = 4a^2</span>  and  <span class=\"katex--inline\">(ax-y)^2 = a^2</span> , where  <span class=\"katex--inline\">a</span>  is a positive real number. What is the area of this region in terms of  <span class=\"katex--inline\">a</span> , valid for all  <span class=\"katex--inline\">a &gt; 0</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~\\frac{8a^2}{(a+1)^2}\\qquad\\textbf{(B)} ~\\frac{4a}{a+1}\\qquad\\textbf{(C)} ~\\frac{8a}{a+1}\\qquad\\textbf{(D)} ~\\frac{8a^2}{a^2+1}\\qquad\\textbf{(E)} ~\\frac{8a}{a^2+1}</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": "2021 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10A_p25", "prev": "/problem/21_amc10A_p23"}}