  Thermal gas in the center of galaxy clusters can show substantial motions
that generate surface-brightness and temperature discontinuities known as cold
fronts. The motions may be triggered by minor or off-axis mergers that preserve
the cool core of the system. The dynamics of the thermal gas can also generate
radio emission from the intra-cluster medium (ICM) and impact the evolution of
clusters' radio sources. We aim to study the central region of Abell 1775, a
system in an ambiguous dynamical state at $z=0.072$ which is known to host an
extended head-tail radio galaxy, with the goal of investigating the connection
between thermal and nonthermal components in its center. We made use of a deep
(100 ks) Chandra observation accompanied by LOFAR 144 MHz, GMRT 235 MHz and 610
MHz, and VLA 1.4 GHz radio data. We find a spiral-like pattern in the X-ray
surface brightness that is mirrored in the temperature and pseudo-entropy maps.
Additionally, we characterize an arc-shaped cold front in the ICM. We interpret
these features in the context of a slingshot gas tail scenario. The structure
of the head-tail radio galaxy "breaks" at the position of the cold front,
showing an extension that is detected only at low frequencies, likely due to
its steep and curved spectrum. We speculate that particle reacceleration is
occurring in the outer region of this tail, which in total covers a projected
size of $\sim800$ kpc. We also report the discovery of revived fossil plasma
with ultra-steep spectrum radio emission in the cluster core together with a
central diffuse radio source that is bounded by the arc-shaped cold front. The
results reported in this work demonstrate the interplay between thermal and
nonthermal components in the cluster center and the presence of ongoing
particle reacceleration in the ICM on different scales.
