Radius Small Circle: Measurement & More

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SUMMARY

The discussion focuses on calculating the radius of a small circle inscribed within a square of side length 2 using the Pythagorean theorem. The equation derived is (1-x)² + 1 = (1+x)², leading to the conclusion that the radius x equals 1/4. This mathematical approach effectively demonstrates the relationship between the circle and the square's dimensions.

PREREQUISITES
  • Understanding of the Pythagorean theorem
  • Basic algebraic manipulation
  • Familiarity with geometric concepts of circles and squares
  • Knowledge of quadratic equations
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  • Explore advanced applications of the Pythagorean theorem in geometry
  • Study the properties of inscribed and circumscribed circles
  • Learn about quadratic equations and their solutions
  • Investigate geometric proofs involving circles and polygons
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Mathematics students, geometry enthusiasts, educators teaching geometric principles, and anyone interested in the application of the Pythagorean theorem in real-world scenarios.

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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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