{"status": "success", "data": {"description_md": "**This was an improvised tie breaker problem to decide the winner in the individual round.**\n\nLet $\\triangle ABC$ be acute-angled with $\\angle ABC = 35^\\circ$. Suppose that $I$ is the incenter of $\\triangle ABC$ and that $AI +AC = BC$. Let $P$ be the point such that $PB$ and $PC$ are tangent to the circumcircle of $\\triangle ABC$. Let $Q$ be the point on the line $AB$ such that $PQ$ is parallel to $AC$. Find $\\angle AQC$ in degrees.", "description_html": "<p><strong>This was an improvised tie breaker problem to decide the winner in the individual round.</strong></p>&#10;<p>Let <span class=\"katex--inline\">\\triangle ABC</span> be acute-angled with <span class=\"katex--inline\">\\angle ABC = 35^\\circ</span>. Suppose that <span class=\"katex--inline\">I</span> is the incenter of <span class=\"katex--inline\">\\triangle ABC</span> and that <span class=\"katex--inline\">AI +AC = BC</span>. Let <span class=\"katex--inline\">P</span> be the point such that <span class=\"katex--inline\">PB</span> and <span class=\"katex--inline\">PC</span> are tangent to the circumcircle of <span class=\"katex--inline\">\\triangle ABC</span>. Let <span class=\"katex--inline\">Q</span> be the point on the line <span class=\"katex--inline\">AB</span> such that <span class=\"katex--inline\">PQ</span> is parallel to <span class=\"katex--inline\">AC</span>. Find <span class=\"katex--inline\">\\angle AQC</span> in degrees.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Christmas Contest Individual Round Tiebreaker", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}