  In this paper, we consider a random geometric graph (RGG)~\(G\) on~\(n\)
nodes with adjacency distance~\(r_n\) just below the Hamiltonicity threshold
and construct Hamiltonian cycles using additional edges called bridges. The
bridges by definition do not belong to~\(G\) and we are interested in
estimating the number of bridges and the maximum bridge length, needed for
constructing a Hamiltonian cycle. In our main result, we show that with high
probability, i.e. with probability converging to one as~\(n \rightarrow
\infty,\) we can obtain a Hamiltonian cycle with maximum bridge length a
constant multiple of~\(r_n\) and containing an arbitrarily small fraction of
edges as bridges. We use a combination of backbone construction and iterative
cycle merging to obtain the desired Hamiltonian cycle.
