{"status": "success", "data": {"description_md": "**POTD May 16, 2024**\n\nLet $ABCD$ be a quadrilateral with an inscribed circle $\\omega$ and let $P$ be the intersection of its diagonals $AC$ and $BD.$ Let $R_1, R_2, R_3, R_4$ be the circumradii of triangles $APB, BPC, CPD, DPA$ respectively. If $R_1 = 31$ and $R_2 = 24$ and $R_3 = 12$, find $R_4$.", "description_html": "<p><strong>POTD May 16, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">ABCD</span> be a quadrilateral with an inscribed circle <span class=\"katex--inline\">\\omega</span> and let <span class=\"katex--inline\">P</span> be the intersection of its diagonals <span class=\"katex--inline\">AC</span> and <span class=\"katex--inline\">BD.</span> Let <span class=\"katex--inline\">R_1, R_2, R_3, R_4</span> be the circumradii of triangles <span class=\"katex--inline\">APB, BPC, CPD, DPA</span> respectively. If <span class=\"katex--inline\">R_1 = 31</span> and <span class=\"katex--inline\">R_2 = 24</span> and <span class=\"katex--inline\">R_3 = 12</span>, find <span class=\"katex--inline\">R_4</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #158", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}