Radius Small Circle: Measurement & More

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Discussion Overview

The discussion revolves around the measurement of the radius of a 'small circle' inscribed within a square with a side length of 2. Participants explore the application of the Pythagorean theorem to derive the radius.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant proposes that if the side of the square is 2, the radius of the small circle, denoted as x, can be derived using the equation $\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$, leading to the conclusion that $\displaystyle x = \frac{1}{4}$.
  • A later reply echoes the initial claim, affirming the solution as a "very good solution".

Areas of Agreement / Disagreement

There appears to be agreement on the proposed solution, but the discussion does not explore any alternative viewpoints or challenge the derivation.

Contextual Notes

The discussion does not address any assumptions or limitations related to the application of the Pythagorean theorem in this context.

Albert1
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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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