{"status": "success", "data": {"description_md": "Two circles of radius $5$ are externally tangent to each other and are internally tangent to a circle of radius $13$ at points $A$ and $B$, as shown in the diagram. The distance $AB$ can be written in the form $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\n\n
\n\n
\n\n$\\textbf{(A) } 21 \\qquad \\textbf{(B) } 29 \\qquad \\textbf{(C) } 58 \\qquad \\textbf{(D) } 69 \\qquad \\textbf{(E) } 93$", "description_html": "

Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points A and B , as shown in the diagram. The distance AB can be written in the form \\tfrac{m}{n} , where m and n are relatively prime positive integers. What is m+n ?

\n
\n\n
\n

\\textbf{(A) } 21 \\qquad \\textbf{(B) } 29 \\qquad \\textbf{(C) } 58 \\qquad \\textbf{(D) } 69 \\qquad \\textbf{(E) } 93

\n

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p16", "prev": "/problem/18_amc10A_p14"}}