Points $(2 ,6 )$ and $(5 ,3 )$ are $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2016-02-27T18:14:17

I have taken you up to the final calculation point

Tony B

$color(blue)("Determine the length AC")$

$AC=sqrt( (x_1-x_2)^2+(y_2-y_1)^2) = sqrt(18)=3sqrt(2)$

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$color(blue)("Determine the length AB")$

$/_ CAB = pi/2-(/_ABC)/2 = pi/2-(3pi)/8 = pi/8 ->(22 1/2 ^o)$

$ABcos(pi/8)= (3sqrt(2))/2$

$AB=(3sqrt(2))/(2cos(pi/8))$
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$color(blue)("To determine arc length")$

This is radius times radian count

$ABxx (3pi)/4 =(3sqrt(2))/(2cos(pi/8)) xx(3pi)/4$

I will let you finish the calculation

Points (2 ,6 )(2 ,6 ) and (5 ,3 )(5 ,3 ) are (3 pi)/4 (3 pi)/4 radians apart on a circle. What is the shortest arc length between the points?