Find the circumference of a circle whose diameter has endpoints at (2 , 1) and (4 , 5).

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You need to remember that the endpoints of diameter lie on circle. Since you know coordinates of endpoints of diameter you may evaluate how long it is such that:`d=sqrt((2-4)^2+(1-5)^2)` .

`d=sqrt((-2)^2+(-4)^2) =gt d=sqrt(4+16) =gt d=sqrt20` `=gt d=sqrt(2^2*5)=gtd=2sqrt5`

Since the formula of circumference comprises the length of radius of circle, hence you may find the...

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You need to remember that the endpoints of diameter lie on circle. Since you know coordinates of endpoints of diameter you may evaluate how long it is such that:`d=sqrt((2-4)^2+(1-5)^2)` .

`d=sqrt((-2)^2+(-4)^2) =gt d=sqrt(4+16) =gt d=sqrt20` `=gt d=sqrt(2^2*5)=gtd=2sqrt5`

Since the formula of circumference comprises the length of radius of circle, hence you may find the radius as half of diameter length.

`r=d/2=gtr=sqrt5`

You may evaluate circumference of circle such that:

circumference=`2r*pi `

Substituting `sqrt5`  for r yields: circumference=`2sqrt5*pi` .

Hence, evaluating the circumference of circle yields circumference=`2sqrt5*pi ` units.

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