{"status": "success", "data": {"description_md": "\n\n\nSquare $ABCD$ has side length $13$ and point $E$ is constructed such that $BE=7$ and $DE=17$. If the sum of all possible values of $AE$ is $k$, find $k^2$.\n\n$\\textbf{(A)}~50\\qquad\\textbf{(B)}~98\\qquad\\textbf{(C)}~288\\qquad\\textbf{(D)}~338\\qquad\\textbf{(E)}~578$", "description_html": "<p>Square <span class=\"katex--inline\">ABCD</span> has side length <span class=\"katex--inline\">13</span> and point <span class=\"katex--inline\">E</span> is constructed such that <span class=\"katex--inline\">BE=7</span> and <span class=\"katex--inline\">DE=17</span>. If the sum of all possible values of <span class=\"katex--inline\">AE</span> is <span class=\"katex--inline\">k</span>, find <span class=\"katex--inline\">k^2</span>.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~50\\qquad\\textbf{(B)}~98\\qquad\\textbf{(C)}~288\\qquad\\textbf{(D)}~338\\qquad\\textbf{(E)}~578</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2024 Mock AMC 12 - Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/2024_mock_amc12-p21", "prev": "/problem/2024_mock_amc12-p19"}}