A circle's center is at (2 ,7 ) and it passes through (3 ,1 ). What is the length of an arc covering (2pi ) /3 radians on the circle?

1 Answer
Alan P.
Jan 27, 2016

Arc length: (2sqrt(37)pi)/3

Explanation:

Part 1:
If the circle has center at (2,7) and passes through (3,1), its radius is:
color(white)("XXX")r=sqrt((2-3)^2+(7-1)^2) = sqrt((-1)^2+6^2) = sqrt(37

Part 2:
For a circle with radius r
color(white)("XXX")"angle" = 2pi rarr "arc length" = 2pir (circumference of circle)
color(white)("XXX")"angle" = pi rarr "arc length" = pir
color(white)("XXX")"angle" =2/3pi rarr "arc length" = 2/3 pir

Solution
A arc with radius sqrt(37) (from Part 1) and an angle of (2pi)/3
will have an arc length of 2/3pisqrt(37)= (2sqrt(37))/3pi

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