AMC 12 2019a Problem 18

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?

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