A circle's center is at #(5 ,2 )# and it passes through #(2 ,7 )#. What is the length of an arc covering #(7pi ) /8 # radians on the circle?

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Answer 1 · 2016-04-07T09:04:22

Length of arc #s=16.0287" "#

Compute the radius #r# first

Let Center point #O(x_o, y_o)=(5, 2)#
Let the other point #A(x_a, y_a)=(2, 7)#

#r=sqrt((x_a-x_o)^2+(y_a-y_o)^2)#
#r=sqrt(34)#

Using the given central angle #theta=(7pi)/8# compute the length of arc

#s=rtheta#
#s=(7sqrt(34)*pi)/8#

God bless....I hope the explanation is useful.