{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be an acute scalene triangle with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ onto lines $AB$ and $AC$, respectively. Suppose $BT=CT=16$, $BC=22$, and $TX^2+TY^2+XY^2=1143$. Find $XY^2$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Let <span class=\"katex--inline\">\\triangle ABC</span> be an acute scalene triangle with circumcircle <span class=\"katex--inline\">\\omega</span>. The tangents to <span class=\"katex--inline\">\\omega</span> at <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span> intersect at <span class=\"katex--inline\">T</span>. Let <span class=\"katex--inline\">X</span> and <span class=\"katex--inline\">Y</span> be the projections of <span class=\"katex--inline\">T</span> onto lines <span class=\"katex--inline\">AB</span> and <span class=\"katex--inline\">AC</span>, respectively. Suppose <span class=\"katex--inline\">BT=CT=16</span>, <span class=\"katex--inline\">BC=22</span>, and <span class=\"katex--inline\">TX^2+TY^2+XY^2=1143</span>. Find <span class=\"katex--inline\">XY^2</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 6, "problem_name": "2020 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/20_aime_II_p14"}}