{"status": "success", "data": {"description_md": "Let $ABC$ be a triangle such that $\\angle ACB = 90^\\circ$. The point $D$ lies inside triangle $ABC$ and on the circle with centre $B$ that passes through $C$. The point $E$ lies on the side $AB$ such that $\\angle DAE = \\angle BDE$. The circle with centre $A$ that passes through $C$ meets the line through $D$ and $E$ at the point $F$, where $E$ lies between $D$ and $F$. If $\\angle ABF = 20^\\circ$, find $\\angle AFE$.", "description_html": "<p>Let <span class=\"katex--inline\">ABC</span> be a triangle such that <span class=\"katex--inline\">\\angle ACB = 90^\\circ</span>. The point <span class=\"katex--inline\">D</span> lies inside triangle <span class=\"katex--inline\">ABC</span> and on the circle with centre <span class=\"katex--inline\">B</span> that passes through <span class=\"katex--inline\">C</span>. The point <span class=\"katex--inline\">E</span> lies on the side <span class=\"katex--inline\">AB</span> such that <span class=\"katex--inline\">\\angle DAE = \\angle BDE</span>. The circle with centre <span class=\"katex--inline\">A</span> that passes through <span class=\"katex--inline\">C</span> meets the line through <span class=\"katex--inline\">D</span> and <span class=\"katex--inline\">E</span> at the point <span class=\"katex--inline\">F</span>, where <span class=\"katex--inline\">E</span> lies between <span class=\"katex--inline\">D</span> and <span class=\"katex--inline\">F</span>. If <span class=\"katex--inline\">\\angle ABF = 20^\\circ</span>, find <span class=\"katex--inline\">\\angle AFE</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Christmas Contest - Individual Round - Problem 20", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/christmas1_individual-p19"}}