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.
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