on circle lie 2n distinct point follow property choose 3 chord connect 3 disjoint pair point point strictly inside circle belong 3 chord the point number 1 2 dot 2n clockwise orderinitially k chord connect k pair point way 2k endpoint chord distinctyou want draw n k additional chord connect remain 2n k point point endpoint exactly chordin end let x total number intersection n chord Compute maximum value x attain choose n k chord optimallyNote exact position 2n point relevant long property state paragraph hold