{"status": "success", "data": {"description_md": "A point P is chosen at random in the interior of equilateral triangle $ABC$. What is the probability that $\\triangle ABP$ has a greater area than each of $\\triangle ACP$ and $\\triangle BCP$?\n\n$\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{4}\\qquad\\textbf{(C)}\\ \\frac{1}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ \\frac{2}{3}$\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 P is chosen at random in the interior of equilateral triangle  <span class=\"katex--inline\">ABC</span> . What is the probability that  <span class=\"katex--inline\">\\triangle ABP</span>  has a greater area than each of  <span class=\"katex--inline\">\\triangle ACP</span>  and  <span class=\"katex--inline\">\\triangle BCP</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{4}\\qquad\\textbf{(C)}\\ \\frac{1}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ \\frac{2}{3}</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": "2003 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p17", "prev": "/problem/03_amc12A_p15"}}