{"status": "success", "data": {"description_md": "Points $A$ and $C$ lie on a circle centered at $O$, each of $\\overline{BA}$ and $\\overline{BC}$ are tangent to the circle, and $\\triangle ABC$ is equilateral. The circle intersects $\\overline{BO}$ at $D$. What is $\\frac{BD}{BO}$?\n\n$\\text{(A) } \\frac {\\sqrt2}{3}\n\\qquad\n\\text{(B) } \\frac {1}{2}\n\\qquad\n\\text{(C) } \\frac {\\sqrt3}{3}\n\\qquad\n\\text{(D) } \\frac {\\sqrt2}{2}\n\\qquad\n\\text{(E) } \\frac {\\sqrt3}{2}$", "description_html": "<p>Points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">C</span>  lie on a circle centered at  <span class=\"katex--inline\">O</span> , each of  <span class=\"katex--inline\">\\overline{BA}</span>  and  <span class=\"katex--inline\">\\overline{BC}</span>  are tangent to the circle, and  <span class=\"katex--inline\">\\triangle ABC</span>  is equilateral. The circle intersects  <span class=\"katex--inline\">\\overline{BO}</span>  at  <span class=\"katex--inline\">D</span> . What is  <span class=\"katex--inline\">\\frac{BD}{BO}</span> ?</p>\n<p> <span class=\"katex--inline\">\\text{(A) } \\frac {\\sqrt2}{3}\n\\qquad\n\\text{(B) } \\frac {1}{2}\n\\qquad\n\\text{(C) } \\frac {\\sqrt3}{3}\n\\qquad\n\\text{(D) } \\frac {\\sqrt2}{2}\n\\qquad\n\\text{(E) } \\frac {\\sqrt3}{2}</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 16", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10B_p17", "prev": "/problem/09_amc10B_p15"}}