{"status": "success", "data": {"description_md": "An annulus is the region between two concentric circles. The concentric circles in the figure have radii $b$ and $c$, with $b>c$. Let $OX$ be a radius of the larger circle, let $XZ$ be tangent to the smaller circle at $Z$, and let $OY$ be the radius of the larger circle that contains $Z$. Let $a=XZ$, $d=YZ$, and $e=XY$. What is the area of the annulus?\n\n
\n\n

\n\n$\\mathrm{(A) \\ } \\pi a^2 \\qquad \\mathrm{(B) \\ } \\pi b^2 \\qquad \\mathrm{(C) \\ } \\pi c^2 \\qquad \\mathrm{(D) \\ } \\pi d^2 \\qquad \\mathrm{(E) \\ } \\pi e^2$\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": "

An annulus is the region between two concentric circles. The concentric circles in the figure have radii b and c, with b>c. Let OX be a radius of the larger circle, let XZ be tangent to the smaller circle at Z, and let OY be the radius of the larger circle that contains Z. Let a=XZ, d=YZ, and e=XY. What is the area of the annulus?


\\mathrm{(A) \\ } \\pi a^2 \\qquad \\mathrm{(B) \\ } \\pi b^2 \\qquad \\mathrm{(C) \\ } \\pi c^2 \\qquad \\mathrm{(D) \\ } \\pi d^2 \\qquad \\mathrm{(E) \\ } \\pi e^2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p13", "prev": "/problem/04_amc10B_p11"}}