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P = I ( 1 + y'^2 )^1/2 dx

Where: I - Integral (from point a to point b)

suppose the circle is x^2 +y^2 + a^2

the perimetr will be 4 times the perimeter in the first quadrant

now take a small element

ds on the curve

by Pythagoras theorm

ds2 = dx2 + dy2

now rearange

to get the formula on top

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