{"status": "success", "data": {"description_md": "Let $S$ be a square of side length $1$.  Two points are chosen independently at random on the sides of $S$.  The probability that the straight-line distance between the points is at least $\\dfrac{1}{2}$ is $\\dfrac{a-b\\pi}{c}$, where $a$, $b$, and $c$ are positive integers with $\\gcd(a,b,c)=1$.  What is $a+b+c$?\n\n$\\textbf{(A) }59\\qquad\\textbf{(B) }60\\qquad\\textbf{(C) }61\\qquad\\textbf{(D) }62\\qquad\\textbf{(E) }63$", "description_html": "<p>Let <span class=\"katex--inline\">S</span> be a square of side length <span class=\"katex--inline\">1</span>.  Two points are chosen independently at random on the sides of <span class=\"katex--inline\">S</span>.  The probability that the straight-line distance between the points is at least <span class=\"katex--inline\">\\dfrac{1}{2}</span> is <span class=\"katex--inline\">\\dfrac{a-b\\pi}{c}</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are positive integers with <span class=\"katex--inline\">\\gcd(a,b,c)=1</span>.  What is <span class=\"katex--inline\">a+b+c</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) }59\\qquad\\textbf{(B) }60\\qquad\\textbf{(C) }61\\qquad\\textbf{(D) }62\\qquad\\textbf{(E) }63</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2015 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/15_amc10A_p24"}}