A circle's center is at $(1 ,5 )$ and it passes through $(2 ,3 )$ . What is the length of an arc covering $(pi ) /4$ radians on the circle?

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Answer 1 · 2016-01-28T04:14:12

$( sqrt(5) pi ) / 4$

Please check my solution here for a detailed explanation.

Solution
Radius $r = sqrt( (2 - 1)^2 + (3 - 5)^2 ) = sqrt(5)$ .
Arc length $S = ( sqrt(5) pi ) / 4$ .

A circle's center is at (1 ,5 )(1 ,5 ) and it passes through (2 ,3 )(2 ,3 ). What is the length of an arc covering (pi ) /4 (pi ) /4 radians on the circle?