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? $\textbf{(A) } 2\sqrt{3} \qquad$ $ \textbf{(B) }4 \qquad$ $ \textbf{(C) } 3\sqrt{2} \qquad$ $ \textbf{(D) } 2\sqrt{5} \qquad$ $ \textbf{(E) } 5$