{"status": "success", "data": {"description_md": "In the diagram, right-angled triangles $AED$ and $BFC$ are constructed inside rectangle $ABCD$ so that $F$ lies on $DE$. If $AE = 21$, $ED = 72$ and $BF = 45$, what is the length of $AB$?\n\n<center><img class=\"problem-image\" src=\"/static/pascal/2005/crops/05_pascal_p25_fig.png\" alt=\"figure\" width=\"336\"></center>\n\n$\\text{(A)}\\ 50\\qquad\\text{(B)}\\ 48\\qquad\\text{(C)}\\ 52\\qquad\\text{(D)}\\ 54\\qquad\\text{(E)}\\ 56$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>In the diagram, right-angled triangles <span class=\"katex--inline\">AED</span> and <span class=\"katex--inline\">BFC</span> are constructed inside rectangle <span class=\"katex--inline\">ABCD</span> so that <span class=\"katex--inline\">F</span> lies on <span class=\"katex--inline\">DE</span>. If <span class=\"katex--inline\">AE = 21</span>, <span class=\"katex--inline\">ED = 72</span> and <span class=\"katex--inline\">BF = 45</span>, what is the length of <span class=\"katex--inline\">AB</span>?</p>\n<center><img class=\"problem-image\" src=\"/static/pascal/2005/crops/05_pascal_p25_fig.png\" alt=\"figure\" width=\"336\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 50\\qquad\\text{(B)}\\ 48\\qquad\\text{(C)}\\ 52\\qquad\\text{(D)}\\ 54\\qquad\\text{(E)}\\ 56</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Pascal</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2005 Pascal Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/05_pascal_p24"}}