{"status": "success", "data": {"description_md": "In $\\triangle BAC$, $\\angle BAC=40^\\circ$, $AB=10$, and $AC=6$.  Points $D$ and $E$ lie on $\\overline{AB}$ and $\\overline{AC}$ respectively.  What is the minimum possible value of $BE+DE+CD$?\n\n$\\textbf{(A) }6\\sqrt 3+3\\qquad<br>\\textbf{(B) }\\dfrac{27}2\\qquad<br>\\textbf{(C) }8\\sqrt 3\\qquad<br>\\textbf{(D) }14\\qquad<br>\\textbf{(E) }3\\sqrt 3+9\\qquad$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle BAC</span> ,  <span class=\"katex--inline\">\\angle BAC=40^\\circ</span> ,  <span class=\"katex--inline\">AB=10</span> , and  <span class=\"katex--inline\">AC=6</span> .  Points  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span>  lie on  <span class=\"katex--inline\">\\overline{AB}</span>  and  <span class=\"katex--inline\">\\overline{AC}</span>  respectively.  What is the minimum possible value of  <span class=\"katex--inline\">BE+DE+CD</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }6\\sqrt 3+3\\qquad\\textbf{(B) }\\dfrac{27}2\\qquad\\textbf{(C) }8\\sqrt 3\\qquad\\textbf{(D) }14\\qquad\\textbf{(E) }3\\sqrt 3+9\\qquad</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p21", "prev": "/problem/14_amc12A_p19"}}