  A Poisson line tessellation is observed within a window. With each cell of
the tessellation, we associate the inradius, which is the radius of the largest
ball contained in the cell. Using Poisson approximation, we compute the limit
distributions of the largest and smallest order statistics for the inradii of
all cells whose nuclei are contained in the window in the limit as the window
is scaled to infinity. We additionally prove that the limit shape of the cells
minimising the inradius is a triangle.
