MathDB

10

Part of 1969 Canada National Olympiad

Problems(1)

Isosceles right triangle

Source: Canada 1969, Problem 10

5/14/2006
Let ABCABC be the right-angled isosceles triangle whose equal sides have length 1. PP is a point on the hypotenuse, and the feet of the perpendiculars from PP to the other sides are QQ and RR. Consider the areas of the triangles APQAPQ and PBRPBR, and the area of the rectangle QCRPQCRP. Prove that regardless of how PP is chosen, the largest of these three areas is at least 2/92/9.
geometryrectangle