A circle's center is at $(2 ,6 )$ and it passes through $(3 ,1 )$ . What is the length of an arc covering $(2pi ) /3$ radians on the circle?

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Answer 1 · 2016-01-27T03:11:38

$( 2 sqrt(26) pi ) / 3$

Please check my solution here for a detailed explanation.

Solution
Radius $r = sqrt( (3 - 2)^2 + (1 - 6)^2 ) = sqrt(26)$ .
Arc length $L = ( 2 sqrt(26) pi ) / 3$ .

A circle's center is at (2 ,6 )(2 ,6 ) and it passes through (3 ,1 )(3 ,1 ). What is the length of an arc covering (2pi ) /3 (2pi ) /3 radians on the circle?