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Question Number 82499 by Maclaurin Stickket last updated on 21/Feb/20

Commented by Maclaurin Stickket last updated on 21/Feb/20

$$ABCDisasquarewithside1.$$$$Thecirclesarecongruent.$$$$ACisthediagonalofsquare.$$$$Findtheradiusr.$$

Commented by Maclaurin Stickket last updated on 21/Feb/20

$$Igotr=\frac{\sqrt{2\sqrt{2}-2}-\sqrt{2\sqrt{2}+2}+2}{4},isthis$$$$right?$$

Commented by mr W last updated on 26/Feb/20

$$\sqrt{2\sqrt{2}+2}-\sqrt{2\sqrt{2}-2}=2\sqrt{\sqrt{2}-1}$$$$r=\frac{\sqrt{2\sqrt{2}-2}-\sqrt{2\sqrt{2}+2}+2}{4}=\frac{2-2\sqrt{\sqrt{2}-1}}{4}$$$$=\frac{1-\sqrt{\sqrt{2}-1}}{2}$$

Answered by mr W last updated on 22/Feb/20

Commented by mr W last updated on 26/Feb/20

$${(1-\frac{2r}{h})}^2=1-\frac{2R}{h}$$$$h=1$$$$R(2+\sqrt{2})=1$$$$R=\frac{2-\sqrt{2}}{2}$$$${(1-2r)}^2=\sqrt{2}-1$$$$\Rightarrow r=\frac{1-\sqrt{\sqrt{2}-1}}{2}\approx 0.178$$

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