{"status": "success", "data": {"description_md": "On the Cartesian plane, let $O$ be the origin and let $A\\neq O$ be on $y=-x^2$. Let the tangents from $A$ to $y=x^2$ intersect $y=x^2$ at $B$ and $C$. If $\\angle BOC = 45^\\circ$. The $y$-coordinate of $A$ can be written as $a-\\sqrt{b}$ for integers $a$ and non-square $b$. Find $|100a|+|b|$.", "description_html": "<p>On the Cartesian plane, let <span class=\"katex--inline\">O</span> be the origin and let <span class=\"katex--inline\">A\\neq O</span> be on <span class=\"katex--inline\">y=-x^2</span>. Let the tangents from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">y=x^2</span> intersect <span class=\"katex--inline\">y=x^2</span> at <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span>. If <span class=\"katex--inline\">\\angle BOC = 45^\\circ</span>. The <span class=\"katex--inline\">y</span>-coordinate of <span class=\"katex--inline\">A</span> can be written as <span class=\"katex--inline\">a-\\sqrt{b}</span> for integers <span class=\"katex--inline\">a</span> and non-square <span class=\"katex--inline\">b</span>. Find <span class=\"katex--inline\">|100a|+|b|</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "Holiday Contest 2025 - Guts Round - Set 8 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}