Friday Puzzler -- Area of the Square

Hint 1

Alex Y

Actually, this is probably not so much a hint as stating the obvious to confirm you are on the right track.

The area of the square is 4*r^2, where r is the radius of the circle. So the problem reduces to finding the radius of the circle.

Re: Hint 1

Henry Higginbotham

This seems too simple to be right, but it looks like A = (2c)^2. No matter how a and b change as the figure moves along the circle, c remains constant. I think.

Correct!

Alex Y

You got the Aha! solution!

C is in fact the radius.

To see that, extend the lines of length a and b and you will see that they are the axes of the circle,and the other diagonal of the rectangle is of length r. And a woodworking connection: how do you "square up" a box or cabinet? Making sure both diagonals are the same! So r=c.

BTW, there MAY be a way using (r-a)^2+(r-b)^2 = c^2, but I sure couldn't get it via that route.