We had this in a quiz, my answer was

but my friends say the answer is 2 = 1 because they squared both sides. but I don't get why the need to square it. so here's the problem.

A square is inscribed in a circle, and another circle is inscribed in the square. What is the ratio of the area of the larger circle to the small circle?

What I did was

Let A1 = large circle

Let A2 = small circle

Radius of large circle:

Radius of small circle:

I then cancel out pi and square leaving the radii.

Thus becomes