{"status": "success", "data": {"description_md": "Circles with centers $O$ and $P$ have radii $2$ and $4$, respectively, and are externally tangent. Points $A$ and $B$ on the circle with center $O$ and points $C$ and $D$ on the circle with center $P$ are such that $AD$ and $BC$ are common external tangents to the circles. What is the area of the concave hexagon $AOBCPD$?\n\n<center>\n<img class=\"problem-image\" height=\"275\" src=\"https://latex.artofproblemsolving.com/f/4/b/f4b71bfd971e24c4e591a7913e1d83e1fa52420b.png\" width=\"335\"/>\n</center>\n\n$\\mathrm{(A) \\ } 18\\sqrt{3}\\qquad \\mathrm{(B) \\ } 24\\sqrt{2}\\qquad \\mathrm{(C) \\ } 36\\qquad \\mathrm{(D) \\ } 24\\sqrt{3}\\qquad \\mathrm{(E) \\ } 32\\sqrt{2}$", "description_html": "<p>Circles with centers  <span class=\"katex--inline\">O</span>  and  <span class=\"katex--inline\">P</span>  have radii  <span class=\"katex--inline\">2</span>  and  <span class=\"katex--inline\">4</span> , respectively, and are externally tangent. Points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  on the circle with center  <span class=\"katex--inline\">O</span>  and points  <span class=\"katex--inline\">C</span>  and  <span class=\"katex--inline\">D</span>  on the circle with center  <span class=\"katex--inline\">P</span>  are such that  <span class=\"katex--inline\">AD</span>  and  <span class=\"katex--inline\">BC</span>  are common external tangents to the circles. What is the area of the concave hexagon  <span class=\"katex--inline\">AOBCPD</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"275\" src=\"https://latex.artofproblemsolving.com/f/4/b/f4b71bfd971e24c4e591a7913e1d83e1fa52420b.png\" width=\"335\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 18\\sqrt{3}\\qquad \\mathrm{(B) \\ } 24\\sqrt{2}\\qquad \\mathrm{(C) \\ } 36\\qquad \\mathrm{(D) \\ } 24\\sqrt{3}\\qquad \\mathrm{(E) \\ } 32\\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": 4, "problem_name": "2006 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10B_p25", "prev": "/problem/06_amc10B_p23"}}