{"status": "success", "data": {"description_md": "A sphere with center $O$ has radius 6. A triangle with sides of length $15$, $15$, and $24$ is situated in space so that each of its sides are tangent to the sphere. What is the distance between $O$ and the plane determined by the triangle?\n\n$\\textbf{(A) } 2\\sqrt{3} \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) } 3\\sqrt{2} \\qquad \\textbf{(D) } 2\\sqrt{5} \\qquad \\textbf{(E) } 5$", "description_html": "<p>A sphere with center  <span class=\"katex--inline\">O</span>  has radius 6. A triangle with sides of length  <span class=\"katex--inline\">15</span> ,  <span class=\"katex--inline\">15</span> , and  <span class=\"katex--inline\">24</span>  is situated in space so that each of its sides are tangent to the sphere. What is the distance between  <span class=\"katex--inline\">O</span>  and the plane determined by the triangle?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2\\sqrt{3} \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) } 3\\sqrt{2} \\qquad \\textbf{(D) } 2\\sqrt{5} \\qquad \\textbf{(E) } 5</span> </p>\n<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": 4, "problem_name": "2019 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10A_p22", "prev": "/problem/19_amc10A_p20"}}