  In this article we study the convex hull spanned by the union of trajectories
of a standard planar Brownian motion, and an independent standard planar
Brownian bridge. We find exact values of the expectation of perimeter and area
of such a convex hull. As an auxiliary result, that is of interest in its own
right, we provide an explicit shape of the probability density function of a
random variable that represents the time when combined maximum of a standard
one-dimensional Brownian motion, and an independent standard one-dimensional
Brownian bridge is attained. At the end, we generalize our results to the case
of multiple independent standard planar Brownian motions and Brownian bridges.
