47th Putnam 1986

Problem B1

ABCD is a rectangle. AEB is isosceles with E on the opposite side of AB to C and D and lies on the circle through A, B, C, D. This circle has radius 1. For what values of |AD| do the rectangle and triangle have the same area?



Answer: 2/5.


The height of E above AB is 1 - AD/2. Hence (1 - AD/2) = 2 AD.



47th Putnam 1986

© John Scholes
30 Sep 1999