{"status": "success", "data": {"description_md": "A number of linked rings, each 1 cm thick, are hanging on a peg. The top ring has an outside diameter of 20 cm. The outside diameter of each of the outer rings is 1 cm less than that of the ring above it. The bottom ring has an outside diameter of 3 cm. What is the distance, in cm, from the top of the top ring to the bottom of the bottom ring?<br><!-- $$[[Image:2006_AMC10A-14.png]]$$ --><br><center><img class=\"problem-image\" alt=\"[asy] size(7cm); pathpen = linewidth(0.7); D(CR((0,0),10)); D(CR((0,0),9.5)); D(CR((0,-18.5),9.5)); D(CR((0,-18.5),9)); MP(&quot;$\u000bdots$&quot;,(0,-31),(0,0)); D(CR((0,-39),3)); D(CR((0,-39),2.5)); D(CR((0,-43.5),2.5)); D(CR((0,-43.5),2)); D(CR((0,-47),2)); D(CR((0,-47),1.5)); D(CR((0,-49.5),1.5)); D(CR((0,-49.5),1.0));  D((12,-10)--(12,10)); MP('20',(12,0),E); D((12,-51)--(12,-48)); MP('3',(12,-49.5),E);[/asy]\" class=\"latexcenter\" height=\"332\" src=\"https://latex.artofproblemsolving.com/7/5/b/75b3e762b96f49323740d90a83fdb1339789180e.png\" width=\"148\"/></center>\n\n$\\mathrm{(A) \\ } 171\\qquad \\mathrm{(B) \\ } 173\\qquad \\mathrm{(C) \\ } 182\\qquad \\mathrm{(D) \\ } 188\\qquad \\mathrm{(E) \\ }  210$\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 number of linked rings, each 1 cm thick, are hanging on a peg. The top ring has an outside diameter of 20 cm. The outside diameter of each of the outer rings is 1 cm less than that of the ring above it. The bottom ring has an outside diameter of 3 cm. What is the distance, in cm, from the top of the top ring to the bottom of the bottom ring?<br/><!-- $$[[Image:2006_AMC10A-14.png]]$$ --><br/><center><img class=\"latexcenter\" alt=\"[asy] size(7cm); pathpen = linewidth(0.7); D(CR((0,0),10)); D(CR((0,0),9.5)); D(CR((0,-18.5),9.5)); D(CR((0,-18.5),9)); MP(&#34;$&#11;dots$&#34;,(0,-31),(0,0)); D(CR((0,-39),3)); D(CR((0,-39),2.5)); D(CR((0,-43.5),2.5)); D(CR((0,-43.5),2)); D(CR((0,-47),2)); D(CR((0,-47),1.5)); D(CR((0,-49.5),1.5)); D(CR((0,-49.5),1.0));  D((12,-10)--(12,10)); MP('20',(12,0),E); D((12,-51)--(12,-48)); MP('3',(12,-49.5),E);[/asy]\" height=\"332\" src=\"https://latex.artofproblemsolving.com/7/5/b/75b3e762b96f49323740d90a83fdb1339789180e.png\" width=\"148\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 171\\qquad \\mathrm{(B) \\ } 173\\qquad \\mathrm{(C) \\ } 182\\qquad \\mathrm{(D) \\ } 188\\qquad \\mathrm{(E) \\ }  210</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": 3, "problem_name": "2006 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12A_p13", "prev": "/problem/06_amc12A_p11"}}