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?

Question

How many degrees does the hour hand of a clock turn in 5 minutes?
A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,3 )# and passes through #(2 ,7 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,1 )#. What is the length of...
A circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of...

1697 views around the world

You can reuse this answer
Creative Commons License

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.