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

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bibiloi | Student, Undergraduate | (Level 3) Honors

Posted June 17, 2011 at 1:01 AM via web

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted June 17, 2011 at 1:04 AM (Answer #1)

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We'll recall the identity that gives the circumference of the circle:

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.
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ga345help | High School Teacher | eNotes Newbie

Posted July 31, 2011 at 6:31 AM (Answer #3)

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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)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted February 18, 2012 at 11:01 PM (Answer #4)

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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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