The arctangent law for a certain random time related to a one-dimensional diffusion

For a time-homogeneous, one-dimensional diffusion process $X(t),$ we investigate the distribution of the first instant, after a given time $r,$ at which $X(t)$ exceeds its maximum on the interval $[0,r],$ generalizing a result of Papanicolaou, which is valid for Brownian motion.