Solution: 5*4 - chords
The shortest chord has length 16 and the longest chord is a diameter and has length 20. The in-between chords (lengths 17, 18, and 19) exist in pairs, giving us a total of eight chords of integer length passing through the given point. This is really an existence question. Constructing the actual chords is a tedious project whose aim concerns particular chords which are numerically but not geometrically of any moment.