{"status": "success", "data": {"description_md": "The figure below depicts a regular $7$-gon inscribed in a unit circle.<br><center><img class=\"problem-image\" alt=\"[asy]         import geometry; unitsize(3cm); draw(circle((0,0),1),linewidth(1.5)); for (int i = 0; i &lt; 7; ++i) {   for (int j = 0; j &lt; i; ++j) {     draw(dir(i * 360/7) -- dir(j * 360/7),linewidth(1.5));   } } for(int i = 0; i &lt; 7; ++i) {    dot(dir(i * 360/7),5+black); } [/asy]\" class=\"latexcenter\" height=\"288\" src=\"https://latex.artofproblemsolving.com/9/2/e/92ecdecb16bc7556a4fcda2df737b19e1d80013e.png\" width=\"292\"/></center><br>What is the sum of the $4$th powers of the lengths of all $21$ of its edges and diagonals?\n\n$\\textbf{(A) }49 \\qquad \\textbf{(B) }98 \\qquad \\textbf{(C) }147 \\qquad \\textbf{(D) }168 \\qquad \\textbf{(E) }196$\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>The figure below depicts a regular  <span class=\"katex--inline\">7</span> -gon inscribed in a unit circle.<br/><center><img class=\"latexcenter\" alt=\"[asy]         import geometry; unitsize(3cm); draw(circle((0,0),1),linewidth(1.5)); for (int i = 0; i &lt; 7; ++i) {   for (int j = 0; j &lt; i; ++j) {     draw(dir(i * 360/7) -- dir(j * 360/7),linewidth(1.5));   } } for(int i = 0; i &lt; 7; ++i) {    dot(dir(i * 360/7),5+black); } [/asy]\" height=\"288\" src=\"https://latex.artofproblemsolving.com/9/2/e/92ecdecb16bc7556a4fcda2df737b19e1d80013e.png\" width=\"292\"/></center><br/>What is the sum of the  <span class=\"katex--inline\">4</span> th powers of the lengths of all  <span class=\"katex--inline\">21</span>  of its edges and diagonals?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }49 \\qquad \\textbf{(B) }98 \\qquad \\textbf{(C) }147 \\qquad \\textbf{(D) }168 \\qquad \\textbf{(E) }196</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": "2022 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p25", "prev": "/problem/22_amc12B_p23"}}