{"status": "success", "data": {"description_md": "Three friends are in the park. Bob and Clarise are standing at the same spot and Abe is standing 10 m away. Bob chooses a random direction and walks in this direction until he is 10 m from Clarise. What is the probability that Bob is closer to Abe than Clarise is to Abe?\n\n$\\text{(A)}\\ \\frac{1}{2}\\qquad\\text{(B)}\\ \\frac{1}{3}\\qquad\\text{(C)}\\ \\frac{1}{\\pi}\\qquad\\text{(D)}\\ \\frac{1}{4}\\qquad\\text{(E)}\\ \\frac{1}{6}$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>Three friends are in the park. Bob and Clarise are standing at the same spot and Abe is standing 10 m away. Bob chooses a random direction and walks in this direction until he is 10 m from Clarise. What is the probability that Bob is closer to Abe than Clarise is to Abe?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ \\frac{1}{2}\\qquad\\text{(B)}\\ \\frac{1}{3}\\qquad\\text{(C)}\\ \\frac{1}{\\pi}\\qquad\\text{(D)}\\ \\frac{1}{4}\\qquad\\text{(E)}\\ \\frac{1}{6}</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 Cayley Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/14_cayley_p24", "prev": "/problem/14_cayley_p22"}}