Geometric probability calculation for a triangle

Let $P(L(\omega)\subset \mathbf {D})$ is the probability that a random segment of length $l$ in $\mathbb{R}^{n}$ having a common point with body $\mathbf {D}$ entirely lies in $\mathbf {D}$. In the paper, using a relationship between $P(L(\omega)\subset \mathbf {D}) $ and covariogram of $\mathbf {D}$ the explicit form of $P(L(\omega)\subset \mathbf {D})$ for arbitrary triangle on the plane is obtained.