{"status": "success", "data": {"description_md": "Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way?\n\n\n![[asy] size(200); defaultpen(0.9); real r = 5/dir(54).x, h = 5 tan(54*pi/180); pair A = (5,0), B = A+10*dir(72), C = (0,r+h), E = (-5,0), D = E+10*dir(108); draw(A--B--C--D--E--cycle); label(\"\\(A\\)\",A+(0,-0.5),SSE); label(\"\\(B\\)\",B+(0.5,0),ENE); label(\"\\(C\\)\",C+(0,0.5),N); label(\"\\(D\\)\",D+(-0.5,0),WNW); label(\"\\(E\\)\",E+(0,-0.5),SW); // real l = 5*sqrt(3); pair ab = (h+l)*dir(72), bc = (h+l)*dir(54); pair AB = (ab.y, h-ab.x), BC = (bc.x,h+bc.y), CD = (-bc.x,h+bc.y), DE = (-ab.y, h-ab.x), EA = (0,-l); draw(A--AB--B^^B--BC--C^^C--CD--D^^D--DE--E^^E--EA--A, dashed); // dot(A); dot(B); dot(C); dot(D); dot(E); dot(AB); dot(BC); dot(CD); dot(DE); dot(EA); [/asy]](https://latex.artofproblemsolving.com/a/3/b/a3b1113e62996ab9b1c6c83bc4836bbb32070801.png)\n\n$\\text {(A) } 1 \\qquad \\text {(B) } 2 \\qquad \\text {(C) } 3 \\qquad \\text {(D) } 4 \\qquad \\text {(E) } 5$\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>Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way?</p>&#10;<p><img src=\"https://latex.artofproblemsolving.com/a/3/b/a3b1113e62996ab9b1c6c83bc4836bbb32070801.png\" alt=\"[asy] size(200); defaultpen(0.9); real r = 5/dir(54).x, h = 5 tan(54*pi/180); pair A = (5,0), B = A+10*dir(72), C = (0,r+h), E = (-5,0), D = E+10*dir(108); draw(A--B--C--D--E--cycle); label(&#34;(A)&#34;,A+(0,-0.5),SSE); label(&#34;(B)&#34;,B+(0.5,0),ENE); label(&#34;(C)&#34;,C+(0,0.5),N); label(&#34;(D)&#34;,D+(-0.5,0),WNW); label(&#34;(E)&#34;,E+(0,-0.5),SW); // real l = 5*sqrt(3); pair ab = (h+l)*dir(72), bc = (h+l)*dir(54); pair AB = (ab.y, h-ab.x), BC = (bc.x,h+bc.y), CD = (-bc.x,h+bc.y), DE = (-ab.y, h-ab.x), EA = (0,-l); draw(A--AB--B^B--BC--CC--CD--DD--DE--E^E--EA--A, dashed); // dot(A); dot(B); dot(C); dot(D); dot(E); dot(AB); dot(BC); dot(CD); dot(DE); dot(EA); [/asy]\"/></p>&#10;<p><span class=\"katex--inline\">\\text {(A) } 1 \\qquad \\text {(B) } 2 \\qquad \\text {(C) } 3 \\qquad \\text {(D) } 4 \\qquad \\text {(E) } 5</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2003 AMC 12B Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p11", "prev": "/problem/03_amc12B_p09"}}