{"status": "success", "data": {"description_md": "**POTD April 19, 2024**\n\nGiven a triangle $ABC$, let the tangent lines to the circumcircle of $\\triangle ABC$ at points $A$ and $B$ intersect at point $T$. Line $CT$ intersects the circumcircle for a second time at point $D$. Let the projections of $D$ onto $AB, BC, AC$ be $M, N, P$ respectively. From $M$ draw a line perpendicular to $NP$ intersecting $BC$ at $E$. If $EC = 5$, $EB = 11$, and $\\angle CEP = 120^\\circ$, compute the length of $CP$.", "description_html": "<p><strong>POTD April 19, 2024</strong></p>&#10;<p>Given a triangle <span class=\"katex--inline\">ABC</span>, let the tangent lines to the circumcircle of <span class=\"katex--inline\">\\triangle ABC</span> at points <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span> intersect at point <span class=\"katex--inline\">T</span>. Line <span class=\"katex--inline\">CT</span> intersects the circumcircle for a second time at point <span class=\"katex--inline\">D</span>. Let the projections of <span class=\"katex--inline\">D</span> onto <span class=\"katex--inline\">AB, BC, AC</span> be <span class=\"katex--inline\">M, N, P</span> respectively. From <span class=\"katex--inline\">M</span> draw a line perpendicular to <span class=\"katex--inline\">NP</span> intersecting <span class=\"katex--inline\">BC</span> at <span class=\"katex--inline\">E</span>. If <span class=\"katex--inline\">EC = 5</span>, <span class=\"katex--inline\">EB = 11</span>, and <span class=\"katex--inline\">\\angle CEP = 120^\\circ</span>, compute the length of <span class=\"katex--inline\">CP</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #131", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}