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We report on observations of very high-energy gamma rays from the shell-type supernova remnant Cassiopeia A with the VERITAS stereoscopic array of four imaging atmospheric Cherenkov telescopes in Arizona. The total exposure time for these observation s is 22 hours, accumulated between September and November of 2007. The gamma-ray source associated with the SNR Cassiopeia A was detected above 200 GeV with a statistical significance of 8.3 s.d. The estimated integral flux for this gamma-ray source is about 3% of the Crab-Nebula flux. The photon spectrum is compatible with a power law dN/dE ~ E^(-Gamma) with an index Gamma = 2.61 +/- 0.24(stat) +/- 0.2(sys). The data are consistent with a point-like source. We provide a detailed description of the analysis results, and discuss physical mechanisms that may be responsible for the observed gamma-ray emission.
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