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

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C = pi*D, where D is the diameter of the circle.

We'll calculate the length of the diameter using the formula:D = sqrt[(4-2)^2 + (5-1)^2]

D = sqrt (4 + 16)D = 2sqrt5

**The circumfrence of the circle whose diameter has endpoints at (2 , 1) and (4 , 5) is: C = 2pi*sqrt5.**

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

First, remember that the formula for circumference is: C=2*pi*r, or C=pi*d, where d=diameter of circle.

The distance between the given points can be determined by using the formula:

Distance=Square root of [(difference in x values)^2 + (difference in y values)^2]

Substituting the given values, Distance= square root of [(4-2)^2 + (5-1)^2]

Distance = square root of [2^2 + 4^2]

Distance = square root of (4 + 16)

Distance = square root of 20

Distance = 2*square root of 5

now substituting into the circumference formula,

Circumference = 2*square root of 5*pi;

to expand further, you have 2*2.236*3.143=14.0555 (all approximate values)

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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