  What spectral conditions imply a graph contains a chorded cycle? This
question was asked by R.J. Gould in 2022. We answer three modified versions of
Gould's question by giving tight spectral conditions that imply the existence
of doubly chorded cycle, a doubly chorded cycle with two chords incident to a
vertex, and a doubly chorded cycle on five vertices with two chords incident to
one vertex, in a graph, respectively.
