MathDB

Quadrilateral inside square

Source: Canada 1970, Problem 5

May 14, 2006

inequalities

Problem Statement

A quadrilateral has one vertex on each side of a square of side-length 1. Show that the lengths

a

b

c

and

d

of the sides of the quadrilateral satisfy the inequalities

2\le a^2+b^2+c^2+d^2\le 4.