A perfect square inside a circle and a perfect square

gonnis

A perfect square inside a circle (so the inner square's corners touch the circle) and a perfect square surrounds the circle (so the circle touches the sides of the outer square. Are the extra bits between the inner square and the circle equal to the extra bits between the circle and the outer square?
Im not explaining this very good but hopefully the question makes sense. Don't know how to include a drawing here.
Thanks

barefeet

This looks like a homework question, if so it belongs in another forum I think.
Anyway, do you know the area of a square?
Do you know the area of a circle?

gonnis

No barefeet this isn't a homework problem lol... its just been a while since Ive thought about circles.... Im asking in the context of before pi. OK its grade school question, its sort of stupid, but its legit, please indulge if you don't mind.
(fyi I asked a similarly dull question in gen discussion and they moved it to gen math, so I figured I may as well just post here cuz it would probably get moved lol)
thanks!

Mark44

Mentor
gonnis, why would you think the area between the inner square and the circle would be equal to the area between the circle and the outer square? Have you made an attempt to come up with an answer for yourself?
1. Start with a unit circle centered at the origin. Its equation is x2 + y2 = 1.
2. Inscribe a square inside the circle, then find the coordinates of the corners of the inner square.
3.Circumscribe a larger square around the circle, and find its corner points.
4. From the information obtained, you should be able to find the areas of all of the objects here, and thereby answer your question.

(BTW, "perfect square" is redundant - a square is a square.)

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