  We present the discovery of NGTS-3Ab, a hot Jupiter found transiting the
primary star of an unresolved binary system. We develop a joint analysis of
multi-colour photometry, centroids, radial velocity (RV) cross-correlation
function (CCF) profiles and their bisector inverse slopes (BIS) to disentangle
this three-body system. Data from the Next Generation Transit Survey (NGTS),
SPECULOOS and HARPS are analysed and modelled with our new blendfitter
software. We find that the binary consists of NGTS-3A (G6V-dwarf) and NGTS-3B
(K1V-dwarf) at <1 arcsec separation. NGTS-3Ab orbits every P = 1.675 days. The
planet radius and mass are R_planet = 1.48+-0.37 R_J and M_planet = 2.38+-0.26
M_J, suggesting it is potentially inflated. We emphasise that only combining
all the information from multi-colour photometry, centroids and RV CCF profiles
can resolve systems like NGTS-3. Such systems cannot be disentangled from
single-colour photometry and RV measurements alone. Importantly, the presence
of a BIS correlation indicates a blend scenario, but is not sufficient to
determine which star is orbited by the third body. Moreover, even if no BIS
correlation is detected, a blend scenario cannot be ruled out without further
information. The choice of methodology for calculating the BIS can influence
the measured significance of its correlation. The presented findings are
crucial to consider for wide-field transit surveys, which require wide CCD
pixels (>5 arcsec) and are prone to contamination by blended objects. With TESS
on the horizon, it is pivotal for the candidate vetting to incorporate all
available follow-up information from multi-colour photometry and RV CCF
profiles.
