### 5th Putnam 1942

**Problem A1**

ABCD is a square side 2a with vertices in that order. It rotates in the first quadrant with A remaining on the positive x-axis and B on the positive y-axis. Find the locus of its center.

**Solution**

Answer: the segment (a, a) to (a√2, a√2).

*Easy.*

Let AB make an angle θ with the x-axis. Then we find that the coordinates of the center to be x = y = a cos θ + a sin θ. But a cos θ + a sin θ = a √2 sin(θ + π/4).

5th Putnam 1942

© John Scholes

jscholes@kalva.demon.co.uk

15 Sep 1999