We prove NP-completeness of the following problem: For n given input numbers, decide whether there exists an n-sided, plane, convex polygon that has an inscribed circle and that has the input numbers as side lengths.
Deineko, V. G., Klinz, B., & Woeginger, G. J. (2009). Polygons with inscribed circles and prescribed side lengths. Applied Mathematics Letters, 22(5), 704-706. https://doi.org/10.1016/j.aml.2008.05.002