circlesgeometry
I'm doing a question where I have a circle that is inscribed in a square. In the gap between the outside of the circle and the inside of the square, a 2-by-4 cm rectangle is at the vertex.
I'm supposed to find the area of the circle.
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I know I need to find the radius of the circle to get the area but I'm sure how to get the radius. I wanted to exploit symmetry but I couldn't get it to go anywhere.
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?
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
You can use the Pythagoras Theorem and find the radius of the circle.