{"status": "success", "data": {"description_md": "Let the circle tangent to sides $AB$, $AC$, and internally tangent to the circumcircle of $\\triangle ABC$ intersect $AB$ at $D$. If $AD=239$ and $BC$ is $24$ times the inradius of $\\triangle ABC$, find the remainder when the circumradius of this triangle is divided by $1000$.", "description_html": "<p>Let the circle tangent to sides <span class=\"katex--inline\">AB</span>, <span class=\"katex--inline\">AC</span>, and internally tangent to the circumcircle of <span class=\"katex--inline\">\\triangle ABC</span> intersect <span class=\"katex--inline\">AB</span> at <span class=\"katex--inline\">D</span>. If <span class=\"katex--inline\">AD=239</span> and <span class=\"katex--inline\">BC</span> is <span class=\"katex--inline\">24</span> times the inradius of <span class=\"katex--inline\">\\triangle ABC</span>, find the remainder when the circumradius of this triangle is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 8, "problem_name": "March Break 2024 - Problem 15", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}