1970 Canadian MO Problems/Problem 5
Problem
A quadrilateral has one vertex on each side of a square of side-length 1. Show that the lengths , , and of the sides of the quadrilateral satisfy the inequalities
Solution
Let the quadrilateral be . Suppose is a distance , from the two nearest vertices of the square. Define , , similarly. Then the sum of the squares of the sides of the quadrilateral is . But which is at least and at most . Similarly for the other pairs of terms, and hence proved.
1970 Canadian MO (Problems) | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 6 |