What is the length of each side of a regular octagon inscribed in a circle of ra

What is the length of each side of a regular octagon inscribed in a circle of radius 10 cm?

What is the length of each side of a regular octagon inscribed in a circle of radius 10 cm?

Step 1: Understand that a regular octagon has 8 equal sides.
Step 2: Know that the octagon is inscribed in a circle, meaning all its corners touch the circle.
Step 3: Identify the radius of the circle, which is given as 10 cm.
Step 4: Use the formula for the length of each side of a regular octagon: s = r × √2(1 - cos(π/n)).
Step 5: Substitute the values into the formula: n = 8 (for octagon) and r = 10 cm.
Step 6: Calculate cos(π/8) using a calculator or trigonometric table.
Step 7: Compute 1 - cos(π/8).
Step 8: Multiply the result by √2.
Step 9: Finally, multiply by the radius (10 cm) to find the length of each side.

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