{"status": "success", "data": {"description_md": "In isosceles triangle $\\triangle ABC$, $AB = BC = 5AC$. Let $D$ be a point on the interior of line segment $AB$, such that $CA = CD$. What is the area of $\\triangle BDC$ divided by the area of $\\triangle ADC$?", "description_html": "<p>In isosceles triangle <span class=\"katex--inline\">\\triangle ABC</span>, <span class=\"katex--inline\">AB = BC = 5AC</span>. Let <span class=\"katex--inline\">D</span> be a point on the interior of line segment <span class=\"katex--inline\">AB</span>, such that <span class=\"katex--inline\">CA = CD</span>. What is the area of <span class=\"katex--inline\">\\triangle BDC</span> divided by the area of <span class=\"katex--inline\">\\triangle ADC</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Holiday Contest 2025 - Guts Round - Set 1 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}