{"status": "success", "data": {"description_md": "Circles $A, B$ and $C$ are externally tangent to each other, and internally tangent to circle $D$. Circles $B$ and $C$ are congruent. Circle $A$ has radius $1$ and passes through the center of $D$. What is the radius of circle $B$?\n$$\n<center>\n<img class=\"problem-image\" height=\"285\" src=\"https://latex.artofproblemsolving.com/6/9/6/69677da9f9025d93eca8bc2a4d63d4a3b5b11c9c.png\" width=\"285\"/>\n</center>$$\n\n$\\mathrm{(A) \\ } \\frac23 \\qquad \\mathrm{(B) \\ } \\frac {\\sqrt3}{2} \\qquad \\mathrm{(C) \\ } \\frac78 \\qquad \\mathrm{(D) \\ } \\frac89 \\qquad \\mathrm{(E) \\ } \\frac {1 + \\sqrt3}{3}$", "description_html": "<p>Circles  <span class=\"katex--inline\">A, B</span>  and  <span class=\"katex--inline\">C</span>  are externally tangent to each other, and internally tangent to circle  <span class=\"katex--inline\">D</span> . Circles  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">C</span>  are congruent. Circle  <span class=\"katex--inline\">A</span>  has radius  <span class=\"katex--inline\">1</span>  and passes through the center of  <span class=\"katex--inline\">D</span> . What is the radius of circle  <span class=\"katex--inline\">B</span> ?<br/>\n$$</p>\n<center>\n<img class=\"problem-image\" height=\"285\" src=\"https://latex.artofproblemsolving.com/6/9/6/69677da9f9025d93eca8bc2a4d63d4a3b5b11c9c.png\" width=\"285\"/>\n</center>$$\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac23 \\qquad \\mathrm{(B) \\ } \\frac {\\sqrt3}{2} \\qquad \\mathrm{(C) \\ } \\frac78 \\qquad \\mathrm{(D) \\ } \\frac89 \\qquad \\mathrm{(E) \\ } \\frac {1 + \\sqrt3}{3}</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": "2004 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p24", "prev": "/problem/04_amc10A_p22"}}