PQRS is a convex quadrilateral such that each of the four sides PQ, QR, RS and SP as well as each of the two diagonals PR and QS have rational lengths. The two diagonals intersect at the point N.

Will all the four line segments PN, QN, RN and SN have rational lengths?

If PQRS is a rectangle or parallelogram, then PN, QN, RN and SN will be rational since the diagonals will be bisectors of each other.

Posted by Brian Smith on 2007-10-18 11:16:05