So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is $\pi r^2$, but they wouldn't give me the area of the parts of the square the circle doesn't cover. any help?
[Math] Area of a square using circle
algebra-precalculuscircles
Related Solutions
The coordinates are right, and therefore the distance to the origin is $\sqrt{2(1-r)^2}$, which is $\sqrt{2}(1-r)$, since $r\lt 1$. But this distance is clearly $1+r$. It follows that $$\sqrt{2}(1-r)=1+r.$$ This is a linear equation in $r$. Solve, and perhaps simplify.
A figure helps a lot. The three segments labeled $r$ are all radii of the small circle. The diagonal of the square is $r\sqrt 2$, so $r(1+\sqrt 2)=x$ No, the tangency points do not bisect the radii of the big circle, they cut them in ratio $1: \sqrt 2$
Best Answer
Hint: Think about the relationship between the radius of the circle, the diameter of the circle, and the side length of the square.
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Do you know the area of a square given its side length?