A circle's center is at $(1 ,2 )$ and it passes through $(5 ,7 )$ . What is the length of an arc covering $(5pi ) /3$ radians on the circle?

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Answer 1 · 2016-01-27T03:06:56

$( 5 sqrt(41) pi ) / 3$

Please check my solution here for a detailed explanation.

Solution
Radius $r = sqrt( (5 - 1)^2 + (7 - 2)^2 ) = sqrt(41)$ .
Arc length $L = ( 5 sqrt(41) pi ) / 3$ .

A circle's center is at (1 ,2 )(1 ,2 ) and it passes through (5 ,7 )(5 ,7 ). What is the length of an arc covering (5pi ) /3 (5pi ) /3 radians on the circle?