### 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?

**Solution**

Answer: 2/5.

*Trivial.*

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

47th Putnam 1986

© John Scholes

jscholes@kalva.demon.co.uk

30 Sep 1999