What is the length of the side of a square inscribed in a circle of radius 5?

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Question: What is the length of the side of a square inscribed in a circle of radius 5?

Options:

Correct Answer: 5√2

Solution:

The diagonal of the square equals the diameter of the circle. Diagonal = 2 × radius = 10. Side = diagonal/√2 = 10/√2 = 5√2.

What is the length of the side of a square inscribed in a circle of radius 5?

What is the length of the side of a square inscribed in a circle of radius 5?

Step 1: Understand that a square can be inscribed in a circle, meaning all corners of the square touch the circle.
Step 2: Know that the radius of the circle is given as 5.
Step 3: Calculate the diameter of the circle. The diameter is twice the radius: Diameter = 2 × radius = 2 × 5 = 10.
Step 4: Recognize that the diagonal of the square is equal to the diameter of the circle. So, the diagonal of the square is also 10.
Step 5: Use the relationship between the side of the square and its diagonal. The formula is: Diagonal = side × √2.
Step 6: Rearrange the formula to find the side of the square: side = diagonal / √2.
Step 7: Substitute the diagonal value into the formula: side = 10 / √2.
Step 8: Simplify the expression: side = 10 / √2 = 5√2.

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