{"status": "success", "data": {"description_md": "A point $P$ is randomly selected from the rectangular region with vertices $(0,0),(2,0),(2,1),(0,1)$. What is the probability that $P$ is closer to the origin than it is to the point $(3,1)$?\n\n$\\mathrm{(A)}\\ \\frac 12<br>\\qquad\\mathrm{(B)}\\ \\frac 23<br>\\qquad\\mathrm{(C)}\\ \\frac 34<br>\\qquad\\mathrm{(D)}\\ \\frac 45<br>\\qquad\\mathrm{(E)}\\ 1$\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>A point  <span class=\"katex--inline\">P</span>  is randomly selected from the rectangular region with vertices  <span class=\"katex--inline\">(0,0),(2,0),(2,1),(0,1)</span> . What is the probability that  <span class=\"katex--inline\">P</span>  is closer to the origin than it is to the point  <span class=\"katex--inline\">(3,1)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac 12\\qquad\\mathrm{(B)}\\ \\frac 23\\qquad\\mathrm{(C)}\\ \\frac 34\\qquad\\mathrm{(D)}\\ \\frac 45\\qquad\\mathrm{(E)}\\ 1</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 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p19", "prev": "/problem/02_amc12B_p17"}}