{"status": "success", "data": {"description_md": "Let $C_1$ and $C_2$ be circles defined by $(x-10)^2 + y^2 = 36$ and $(x+15)^2 + y^2 = 81$<br>respectively. What is the length of the shortest line segment $PQ$ that is tangent to $C_1$ at $P$ and to $C_2$ at $Q$?\n\n$\\text{(A) }15<br>\\qquad<br>\\text{(B) }18<br>\\qquad<br>\\text{(C) }20<br>\\qquad<br>\\text{(D) }21<br>\\qquad<br>\\text{(E) }24$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">C_1</span>  and  <span class=\"katex--inline\">C_2</span>  be circles defined by  <span class=\"katex--inline\">(x-10)^2 + y^2 = 36</span>  and  <span class=\"katex--inline\">(x+15)^2 + y^2 = 81</span> <br/>respectively. What is the length of the shortest line segment  <span class=\"katex--inline\">PQ</span>  that is tangent to  <span class=\"katex--inline\">C_1</span>  at  <span class=\"katex--inline\">P</span>  and to  <span class=\"katex--inline\">C_2</span>  at  <span class=\"katex--inline\">Q</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\text{(A) }15\\qquad\\text{(B) }18\\qquad\\text{(C) }20\\qquad\\text{(D) }21\\qquad\\text{(E) }24</span> </p>&#10;<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": "2002 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p19", "prev": "/problem/02_amc12A_p17"}}