MHB Radius Small Circle: Measurement & More

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The discussion focuses on calculating the radius of a small circle inscribed within a square with a side length of 2. Using the Pythagorean theorem, the relationship between the radius (x) and the square's dimensions is established through the equation (1-x)² + 1 = (1+x)². Solving this equation reveals that the radius x equals 1/4. The solution is confirmed as correct and well-received by participants. The mathematical approach effectively demonstrates the application of Pythagorean theorem in geometric contexts.
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[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
 
hint:
see Ford Circles
 
chisigma said:
[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
very good solution !
 

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