{"status": "success", "data": {"description_md": "Triangle $ABC$ is a right triangle with $\\angle ACB$ as its right angle, $m\\angle ABC = 60^{\\circ}$, and $AB = 10$. Let $P$ be randomly chosen inside $\\triangle ABC$, and extend $\\overline{BP}$ to meet $\\overline{AC}$ at $D$. What is the probability that $BD > 5\\sqrt{2}$?\n\n$\\textbf{(A)}\\ \\frac{2-\\sqrt2}{2}\\qquad\\textbf{(B)}\\ \\frac{1}{3}\\qquad\\textbf{(C)}\\ \\frac{3-\\sqrt3}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ \\frac{5-\\sqrt5}{5}$\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": "

Triangle ABC is a right triangle with \\angle ACB as its right angle, m\\angle ABC = 60^{\\circ} , and AB = 10 . Let P be randomly chosen inside \\triangle ABC , and extend \\overline{BP} to meet \\overline{AC} at D . What is the probability that BD > 5\\sqrt{2} ?

\\textbf{(A)}\\ \\frac{2-\\sqrt2}{2}\\qquad\\textbf{(B)}\\ \\frac{1}{3}\\qquad\\textbf{(C)}\\ \\frac{3-\\sqrt3}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ \\frac{5-\\sqrt5}{5}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2002 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p23", "prev": "/problem/02_amc12A_p21"}}