A circle's center is at (4 ,2 ) and it passes through (6 ,2 ). What is the length of an arc covering (5pi ) /3 radians on the circle?

1 Answer
Anjali G
Jan 7, 2017

The arc length is the fraction of the circle (theta/2pi) times the circumference. The radius is needed to find the circumference, so find the radius by finding the distance between the center and (6,2), a point on the circle.

We could use the distance formula, or picture the distance between (4,2) and (6,2) as 2 units, because the y values of the points are the same.
r=2

Let arc length = s
s=(theta/(2pi))(2pir)
s=thetar

s=(5pi)/3*2

s=(10pi)/3 "units"

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