76th Annual William Lowell Putnam Mathematical Competition

摘要

A1. Let A and B be points on the same branch of the hyperbola xy=1. Suppose that P is a point lying between A and B on this hyperbola, such that the area of the triangle APB is as large as possible. Show that the region bounded by the hyperbola and the chord AP has the same area as the region bounded by the hyperbola and the chord PB.