{"status": "success", "data": {"description_md": "Circle $A$ has radius $100$. Circle $B$ has an integer radius $r<100$ and remains internally tangent to circle $A$ as it rolls once around the circumference of circle $A$. The two circles have the same points of tangency at the beginning and end of circle $B$'s trip. How many possible values can $r$ have?\n\n$\\mathrm{(A)}\\ 4\n\\qquad\n\\mathrm{(B)}\\ 8\n\\qquad\n\\mathrm{(C)}\\ 9\n\\qquad\n\\mathrm{(D)}\\ 50\n\\qquad\n\\mathrm{(E)}\\ 90$", "description_html": "<p>Circle  <span class=\"katex--inline\">A</span>  has radius  <span class=\"katex--inline\">100</span> . Circle  <span class=\"katex--inline\">B</span>  has an integer radius  <span class=\"katex--inline\">r&lt;100</span>  and remains internally tangent to circle  <span class=\"katex--inline\">A</span>  as it rolls once around the circumference of circle  <span class=\"katex--inline\">A</span> . The two circles have the same points of tangency at the beginning and end of circle  <span class=\"katex--inline\">B</span> 's trip. How many possible values can  <span class=\"katex--inline\">r</span>  have?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 4\n\\qquad\n\\mathrm{(B)}\\ 8\n\\qquad\n\\mathrm{(C)}\\ 9\n\\qquad\n\\mathrm{(D)}\\ 50\n\\qquad\n\\mathrm{(E)}\\ 90</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 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p20", "prev": "/problem/09_amc10A_p18"}}