Asymptomatic rhymes with:
symptomatic, symptomatic, symptomatic, symptomatic, automatic, semiautomatic, symptomatic, systematic, aromatic, automatic, axiomatic, cinematic, diagrammatic, diplomatic, dramatic, emblematic, epigrammatic, idiomatic, mathematic, melodramatic, problematic, programmatic, psychosomatic, semiautomatic, symptomatic, systematic, telematic, undiplomatic