{"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 is tangent to the sphere. What is the distance between $O$ and the plane determined by the triangle?\n\n$\\textbf{(A) }2\\sqrt{3}\\qquad<br>\\textbf{(B) }4\\qquad<br>\\textbf{(C) }3\\sqrt{2}\\qquad<br>\\textbf{(D) }2\\sqrt{5}\\qquad<br>\\textbf{(E) }5\\qquad$\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>A sphere with center  <span class=\"katex--inline\">O</span>  has radius  <span class=\"katex--inline\">6</span> . A triangle with sides of length  <span class=\"katex--inline\">15, 15,</span>  and  <span class=\"katex--inline\">24</span>  is situated in space so that each of its sides is tangent to the sphere. What is the distance between  <span class=\"katex--inline\">O</span>  and the plane determined by the triangle?</p>&#10;<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\\qquad</span> </p>&#10;<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": 3, "problem_name": "2019 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p19", "prev": "/problem/19_amc12A_p17"}}