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A square is inscribed in a circle, the diameter is 10 cm. What is length of one side of the sqare ?

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May 21, 2011
Geometry - Square Inscribed in a Circle
by: Staff


The question:

A square is inscribed in a circle, the diameter is 10 cm. What is length of one side of the sqare ?


The answer:

A square is inscribed in a circle, the diameter is 10 cm. What is length of one side of the square?


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When a square is inscribed within a circle, the four corners of the square touch the outline of the circle.

If the diameter of the circle is 10 cm, the diagonal of the square (the distance between two opposite corners) is also 10 cm.



The length of a side of the square can be computed using the Pythagorean Theorem:

If s = the length of one side of the square, and d = the diameter of the circle, then

s² + s² = d²

s² + s² = 10²
2s² = 10²

(2s²)/2 = (10²)/2

(s²)*(2/2) = (10²)/2

(s²)*(1) = (10²)/2

(s²)*1 = (10²)/2

(s²) = (10²)/2

s² = (10²)/2

s² = 100/2

s² = 50

sqrt(s²) = sqrt(50)

s = sqrt(50)

s = sqrt(2*25)

s = sqrt(25)*sqrt(2)

s = 5*sqrt(2)

s = 5*(1.414213562373095)

s = 7.071067811865475

s = 7.07 cm (rounded to the nearest hundredth)

the final answer is: each side of the square = 7.07 cm


Thanks for writing.

Staff
www.solving-math-problems.com



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