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The circumference is pi x diameter

Perimeter of semi circle is (0.5) x pi x diameter + diameter which is

diameter x (0.5pi + 1)

Subtracting Perimeter from Circumference we get

[pi x diameter] - [diameter x (0.5pi + 1)] which is

diameter x [pi - 0.5pi -1]

pi = 3.1415

Hence the result = diameter x (3.1415 - 1.570 - 1) which will always be positive. Hence circumference is greater than perimeter of semi circle.

Intuitively also we see that the diameter is a straight line and the semi circles are arcs over the end points of the diameter.

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Q: Is the circumference of a circle greater than less than or equal to the perimiter of a semi circle?
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