Isosceles right triangle
Source: Canada 1969, Problem 10
May 14, 2006
geometryrectangle
Problem Statement
Let be the right-angled isosceles triangle whose equal sides have length 1. is a point on the hypotenuse, and the feet of the perpendiculars from to the other sides are and . Consider the areas of the triangles and , and the area of the rectangle . Prove that regardless of how is chosen, the largest of these three areas is at least .