{"status": "success", "data": {"description_md": "**POTD January 12, 2023**\nFor $\\triangle ABC$ with all of its points on the parabola $y=x^2$, let $\\delta( \\triangle ABC)$ be the sum of the slopes of lines $AB$, $BC$, and $CA$. \n\nRosalind constructs a $\\triangle XYZ$ such the slope of $\\overline{XY}$ is twice the slope of $\\overline{YZ}$, and the sum of the $x$-coordinates of points $X$ and $Z$ is $\\frac{2023}{\\sqrt{2}}$. Furthermore, over all possible configurations of $\\triangle XYZ$, her construction is the one for which $\\tan(\\angle XYZ)$ is maximized. Find the last three digits of $\\delta(\\triangle XYZ)^2$.", "description_html": "<p><strong>POTD January 12, 2023</strong><br/>&#10;For <span class=\"katex--inline\">\\triangle ABC</span> with all of its points on the parabola <span class=\"katex--inline\">y=x^2</span>, let <span class=\"katex--inline\">\\delta( \\triangle ABC)</span> be the sum of the slopes of lines <span class=\"katex--inline\">AB</span>, <span class=\"katex--inline\">BC</span>, and <span class=\"katex--inline\">CA</span>.</p>&#10;<p>Rosalind constructs a <span class=\"katex--inline\">\\triangle XYZ</span> such the slope of <span class=\"katex--inline\">\\overline{XY}</span> is twice the slope of <span class=\"katex--inline\">\\overline{YZ}</span>, and the sum of the <span class=\"katex--inline\">x</span>-coordinates of points <span class=\"katex--inline\">X</span> and <span class=\"katex--inline\">Z</span> is <span class=\"katex--inline\">\\frac{2023}{\\sqrt{2}}</span>. Furthermore, over all possible configurations of <span class=\"katex--inline\">\\triangle XYZ</span>, her construction is the one for which <span class=\"katex--inline\">\\tan(\\angle XYZ)</span> is maximized. Find the last three digits of <span class=\"katex--inline\">\\delta(\\triangle XYZ)^2</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #38", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}