  We point out an easy link between two striking identities on exponential
functionals of the Wiener process and the Wiener bridge originated by Bougerol,
and Donati-Martin, Matsumoto and Yor, respectively. The link is established
using a continuous one-parameter family of Gaussian processes known as
$\alpha$-Wiener bridges or scaled Wiener bridges, which in case $\alpha=0$
coincides with a Wiener process and for $\alpha=1$ is a version of the Wiener
bridge.
