  We present results obtained from a detailed analysis of a deep Chandra
observation of the bright FR II radio galaxy 3C~444 in Abell~3847 cluster. A
pair of huge X-ray cavities are detected along North and South directions from
the centre of 3C 444. X-ray and radio images of the cluster reveal peculiar
positioning of the cavities and radio bubbles. The radio lobes and X-ray
cavities are apparently not spatially coincident and exhibit offsets by ~61 kpc
and ~77 kpc from each other along the North and South directions, respectively.
Radial temperature and density profiles reveal the presence of a cool core in
the cluster. Imaging and spectral studies showed the removal of substantial
amount of matter from the core of the cluster by the radio jets. A detailed
analysis of the temperature and density profiles showed the presence of a
rarely detected elliptical shock in the cluster. Detection of inflating
cavities at an average distance of ~55 kpc from the centre implies that the
central engine feeds a remarkable amount of radio power (~6.3 X 10^44 erg/s)
into the intra-cluster medium over ~10^8 yr, the estimated age of cavity. The
cooling luminosity of the cluster was estimated to be ~8.30 X 10^43 erg/s,
which confirms that the AGN power is sufficient to quench the cooling. Ratios
of mass accretion rate to Eddington and Bondi rates were estimated to be ~0.08
and 3.5 X 10^4, respectively. This indicates that the black hole in the core of
the cluster accretes matter through chaotic cold accretion.
