  A chorded cycle is a cycle with at least one chord. Gould asked in [Graphs
Comb. 38 (2022) 189] the question: What spectral conditions imply a graph
contains a chorded cycle? For a graph with fixed size, extremal spectral
conditions are given to ensure that a graph contains a chorded cycle and a
$(2k-3)$-chorded $(2k+1)$-cycle for $k\ge 2$, respectively, via spectral
radius.
