{"status": "success", "data": {"description_md": "Triangle $ABC$ with $AB=50$ and $AC=10$ has area $120$. Let $D$ be the midpoint of $\\overline{AB}$, and let $E$ be the midpoint of $\\overline{AC}$. The angle bisector of $\\angle BAC$ intersects $\\overline{DE}$ and $\\overline{BC}$ at $F$ and $G$, respectively. What is the area of quadrilateral $FDBG$?\n\n$\\textbf{(A) }60 \\qquad\n\\textbf{(B) }65 \\qquad\n\\textbf{(C) }70 \\qquad\n\\textbf{(D) }75 \\qquad\n\\textbf{(E) }80 \\qquad$", "description_html": "<p>Triangle  <span class=\"katex--inline\">ABC</span>  with  <span class=\"katex--inline\">AB=50</span>  and  <span class=\"katex--inline\">AC=10</span>  has area  <span class=\"katex--inline\">120</span> . Let  <span class=\"katex--inline\">D</span>  be the midpoint of  <span class=\"katex--inline\">\\overline{AB}</span> , and let  <span class=\"katex--inline\">E</span>  be the midpoint of  <span class=\"katex--inline\">\\overline{AC}</span> . The angle bisector of  <span class=\"katex--inline\">\\angle BAC</span>  intersects  <span class=\"katex--inline\">\\overline{DE}</span>  and  <span class=\"katex--inline\">\\overline{BC}</span>  at  <span class=\"katex--inline\">F</span>  and  <span class=\"katex--inline\">G</span> , respectively. What is the area of quadrilateral  <span class=\"katex--inline\">FDBG</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }60 \\qquad\n\\textbf{(B) }65 \\qquad\n\\textbf{(C) }70 \\qquad\n\\textbf{(D) }75 \\qquad\n\\textbf{(E) }80 \\qquad</span> </p>\n<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": 4, "problem_name": "2018 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p25", "prev": "/problem/18_amc10A_p23"}}