Here's what rhymes with biliaryenteric.
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angelic relic allelic psychedelic evangelic endemic poetic energetic metric pelvic peptic technic benthic eutectic medic fetich pectic aesthetic genetic epidemic acetic majestic pathetic ascetic esthetic septic centric hectic polemic splenic emetic empathetic eugenic pandemic phrenic sceptic totemic acerbic irenic paregoric redbrick bathetic domestic academic electric magnetic sympathetic authentic kinetic prophetic synthetic systemic athletic diabetic dielectric geometric symmetric antigenic forensic ischemic phonetic apathetic aseptic diuretic isometric obstetric biogenic cryogenic neurogenic psychogenic pyogenic skeptic anorexic dietetic geodesic geodetic hermetic allergenic anorectic antithetic leukaemic lovesick diametric gametic parenthetic telegenic phrenetic arithmetic anesthetic dialectic eccentric antiseptic asymmetric concentric cosmetic eclectic epileptic epistemic parametric pathogenic alphabetic anaesthetic prosthetic psychometric transgenic barometric cybernetic ethnocentric frenetic kinesthetic mutagenic photometric teratogenic androgenic dyslexic dyspeptic geocentric inauthentic homiletic paramedic paraplegic photogenic pyrotechnic splenetic thermometric unaesthetic unauthentic exegetic hypoallergenic cliometric copacetic dyslectic apologetic schizophrenic volumetric carcinogenic econometric phylogenetic unsympathetic biosynthetic colorimetric egocentric iatrogenic isoelectric neuroleptic ontogenetic apoplectic neurasthenic nonacademic peripatetic radiometric antipathetic cataleptic polytechnic nonathletic nonelectric unesthetic parasympathetic photoelectric photosynthetic anthropogenic antidiuretic ferromagnetic geomagnetic nonparametric paramagnetic trigonometric hallucinogenic nonmagnetic unapologetic calisthenic narcoleptic telekinetic psychokinetic callisthenic hydroelectric piezoelectric stoichiometric anthropocentric heliocentric onomatopoetic electromagnetic pharmacokinetic