{"status": "success", "data": {"description_md": "In $\\triangle ABC$ with circumcircle $\\omega$ and circumcenter $O$, we have $\\angle A = 60^\\circ$. Let the angle bisector of angle $A$ intersect $\\omega$ again at point $D$ and let line $AO$ intersect $\\omega$ again at point $E$. Given that $BE=DE=3-\\sqrt{3}$, find the area of $ABEC$.", "description_html": "<p>In <span class=\"katex--inline\">\\triangle ABC</span> with circumcircle <span class=\"katex--inline\">\\omega</span> and circumcenter <span class=\"katex--inline\">O</span>, we have <span class=\"katex--inline\">\\angle A = 60^\\circ</span>. Let the angle bisector of angle <span class=\"katex--inline\">A</span> intersect <span class=\"katex--inline\">\\omega</span> again at point <span class=\"katex--inline\">D</span> and let line <span class=\"katex--inline\">AO</span> intersect <span class=\"katex--inline\">\\omega</span> again at point <span class=\"katex--inline\">E</span>. Given that <span class=\"katex--inline\">BE=DE=3-\\sqrt{3}</span>, find the area of <span class=\"katex--inline\">ABEC</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Holiday Contest 2025 - Guts Round - Set 4 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}