{"status": "success", "data": {"description_md": "An object moves $8$ cm in a straight line from $A$ to $B$, turns at an angle $\\alpha$, measured in radians and chosen at random from the interval $(0,\\pi)$, and moves $5$ cm in a straight line to $C$. What is the probability that $AC < 7$?\n\n$\\mathrm{(A)}\\ \\frac{1}{6}\\qquad\\mathrm{(B)}\\ \\frac{1}{5}\\qquad\\mathrm{(C)}\\ \\frac{1}{4}\\qquad\\mathrm{(D)}\\ \\frac{1}{3}\\qquad\\mathrm{(E)}\\ \\frac{1}{2}$\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>An object moves <span class=\"katex--inline\">8</span> cm in a straight line from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">B</span>, turns at an angle <span class=\"katex--inline\">\\alpha</span>, measured in radians and chosen at random from the interval <span class=\"katex--inline\">(0,\\pi)</span>, and moves <span class=\"katex--inline\">5</span> cm in a straight line to <span class=\"katex--inline\">C</span>. What is the probability that <span class=\"katex--inline\">AC &lt; 7</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1}{6}\\qquad\\mathrm{(B)}\\ \\frac{1}{5}\\qquad\\mathrm{(C)}\\ \\frac{1}{4}\\qquad\\mathrm{(D)}\\ \\frac{1}{3}\\qquad\\mathrm{(E)}\\ \\frac{1}{2}</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2003 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p22", "prev": "/problem/03_amc12B_p20"}}