The square and circle below are tangent at one point and meet at four other points, as shown. If the side of the square is 8 units long, what's the radius of the circle?
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I'm pretty sure this question already has an answer here somewhere. I'll see if I can find it. – Blue Aug 22 '19 at 23:00
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1Found it: "Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers". – Blue Aug 22 '19 at 23:03
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1The answer is here https://math.stackexchange.com/questions/3022946/finding-all-possible-proofs – Larry Aug 22 '19 at 23:08
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If Radius, breadth and height are resp $( R, 2b, 2h)$ We have $ \sqrt {b^2+h^2}=R,, b+R= 2 h,$ Eliminate R and solve quadratic equation $ \rightarrow \dfrac{b}{h}= \dfrac34,, \dfrac{b}{R}= \dfrac35,,$ – Narasimham Aug 23 '19 at 01:37