{"status": "success", "data": {"description_md": "Triangle $ABC$ has a right angle at $B$, $AB=1$, and $BC=2$. The angle bisector of $\\angle A$ intersects side $\\overline{BC}$ at $D$. What is $BD$?\n\n<center>\n<img class=\"problem-image\" height=\"125\" src=\"https://latex.artofproblemsolving.com/f/0/b/f0b6594577eb2fc6916bc732b5f99843acda5c60.png\" width=\"222\"/>\n</center>\n\n$\\text{(A) } \\frac {\\sqrt3 - 1}{2}\n\\qquad\n\\text{(B) } \\frac {\\sqrt5 - 1}{2}\n\\qquad\n\\text{(C) } \\frac {\\sqrt5 + 1}{2}\n\\qquad\n\\text{(D) } \\frac {\\sqrt6 + \\sqrt2}{2}\n\\qquad\n\\text{(E) } 2\\sqrt 3 - 1$", "description_html": "<p>Triangle  <span class=\"katex--inline\">ABC</span>  has a right angle at  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">AB=1</span> , and  <span class=\"katex--inline\">BC=2</span> . The angle bisector of  <span class=\"katex--inline\">\\angle A</span>  intersects side  <span class=\"katex--inline\">\\overline{BC}</span>  at  <span class=\"katex--inline\">D</span> . What is  <span class=\"katex--inline\">BD</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"125\" src=\"https://latex.artofproblemsolving.com/f/0/b/f0b6594577eb2fc6916bc732b5f99843acda5c60.png\" width=\"222\"/>\n</center>\n<p> <span class=\"katex--inline\">\\text{(A) } \\frac {\\sqrt3 - 1}{2}\n\\qquad\n\\text{(B) } \\frac {\\sqrt5 - 1}{2}\n\\qquad\n\\text{(C) } \\frac {\\sqrt5 + 1}{2}\n\\qquad\n\\text{(D) } \\frac {\\sqrt6 + \\sqrt2}{2}\n\\qquad\n\\text{(E) } 2\\sqrt 3 - 1</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": 3, "problem_name": "2009 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10B_p21", "prev": "/problem/09_amc10B_p19"}}