23 The points P(p,1/p), Q(q,1/q), R(r,1/r) and S(s,1/s) lie on the curve xy = 1.

PQ RS if and only if pqrs = 1,

Conclude that if a triangle is drawn with its vertices on the rectangular hyperbola: xy = 1, then the altitudes of the triangle intersect at a common point which also lies on the hyperbola (an altitude of a triangle is the perpendicular from a vertex to the opposite side).