construct a rectangle A inside it with maximum area
Source: China TST 1987, problem 4
May 16, 2005
geometryrectangleratioanalytic geometrysymmetryconicshyperbola
Problem Statement
Given a convex figure in the Cartesian plane that is symmetric with respect of both axis, we construct a rectangle inside it with maximum area (over all posible rectangles). Then we enlarge it with center in the center of the rectangle and ratio lamda such that is covers the convex figure. Find the smallest lamda such that it works for all convex figures.