quasi wrote: >Richard Tobin wrote: >>quasi wrote: >> >>>If a pentagon inscribed in a unit circle has rational edge >>>lengths, then for some reordering of the edges within the >>>circle, some diagonal has rational length. >> >>What do you make of >> >> radius 168: 53 91 187 292 294 > >Very close, but it doesn't actually work, at least not with >radius 168. > >The circumradius of a cyclic pentagon with those edge lengths >is a tiny little bit more than 168.
Let r be the actual circumradius of a cyclic pentagon with those edge lengths. Then besides not being equal to 168, r is in fact, irrational.