{"status": "success", "data": {"description_md": "**POTD Challenge December 18, 2023**\n**Author:** awesomeming327\n\nThe ellipse with foci $A$ and $B$ passing through $C$, the ellipse with foci $B$ and $C$ passing through $A$, and the ellipse with foci $C$ and $A$ passing through $B$ concur. If $AB = 4$, $BC = 7$, find the sum of all possible values of $AC^2$.", "description_html": "<p><strong>POTD Challenge December 18, 2023</strong><br/>&#10;<strong>Author:</strong> awesomeming327</p>&#10;<p>The ellipse with foci <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span> passing through <span class=\"katex--inline\">C</span>, the ellipse with foci <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span> passing through <span class=\"katex--inline\">A</span>, and the ellipse with foci <span class=\"katex--inline\">C</span> and <span class=\"katex--inline\">A</span> passing through <span class=\"katex--inline\">B</span> concur. If <span class=\"katex--inline\">AB = 4</span>, <span class=\"katex--inline\">BC = 7</span>, find the sum of all possible values of <span class=\"katex--inline\">AC^2</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Problem of the Day #29 (Challenge)", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}