A circle's center is at #(7 ,2 )# and it passes through #(5 ,6 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?

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Answer 1 · 2016-09-25T09:02:59

#:. "Length of Arc="(7sqrt5pi)/2~~24.59"unit"#.

Let #r# be the radius of the circle.

The Centre C of the circle is #C(7,2)# and, the circle passes through

the pt.#P(5,6)#. Hence, the dist. #CP=r#.

Using the Distance Formula, we get,

#r^2=CP^2=(7-5)^2+(2-6)^2=4+16=20#

#:. r=sqrt20=2sqrt5#.

Hence, the #"Length of Arc CP=s="rtheta#, where, #theta# is the

measure (in Radians ), of the #/_# made by the #"Arc "CP# at the

Centre. We have, #r=2sqrt5, &, theta=(7pi)/4.#

#:. "Length of Arc="2sqrt5*(7pi)/4=(7sqrt5pi)/2~~24.59"unit"#.