{"status": "success", "data": {"description_md": "A plane contains points $A$ and $B$ with $AB = 1$. Let $S$ be the union of all disks of radius $1$ in the plane that cover $\\overline{AB}$. What is the area of $S$?\n\n$\\text {(A) } 2\\pi + \\sqrt3 \\qquad \\text {(B) } \\frac {8\\pi}{3} \\qquad \\text {(C) } 3\\pi - \\frac {\\sqrt3}{2} \\qquad \\text {(D) } \\frac {10\\pi}{3} - \\sqrt3 \\qquad \\text {(E) }4\\pi - 2\\sqrt3$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A plane contains points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  with  <span class=\"katex--inline\">AB = 1</span> . Let  <span class=\"katex--inline\">S</span>  be the union of all disks of radius  <span class=\"katex--inline\">1</span>  in the plane that cover  <span class=\"katex--inline\">\\overline{AB}</span> . What is the area of  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\text {(A) } 2\\pi + \\sqrt3 \\qquad \\text {(B) } \\frac {8\\pi}{3} \\qquad \\text {(C) } 3\\pi - \\frac {\\sqrt3}{2} \\qquad \\text {(D) } \\frac {10\\pi}{3} - \\sqrt3 \\qquad \\text {(E) }4\\pi - 2\\sqrt3</span> </p>&#10;<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": 5, "problem_name": "2004 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p25", "prev": "/problem/04_amc12A_p23"}}