# Help - Geometry

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

### Comments for Help - Geometry

 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? (1) Click the following link to VIEW a DIAGRAM of the PROBLEM; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter: Use the Backspace key to return to this page: http://www.solving-math-problems.com/images/square-inscribed-within-circle.png 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