Points $(8, 5)$ $(8 ,5 )$ and $(3, 4)$ $(3 ,4 )$ are $\frac{π}{3}$ $( pi)/3$ radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2016-02-09T16:15:57

Let me give you a starting point:
Tony B

Distance between $P_{1} and P_{2}$ $P_1" and "P_2$ is

$\sqrt{{(8 - 5)}^{2} + {(5 - 4)}^{2}} = \sqrt{26}$ $sqrt((8-5)^2+(5-4)^2)" "=" "sqrt(26)$

Then use $r sin (\frac{π}{6}) = P_{1} P_{3} = \frac{\sqrt{26}}{2}$ $" "rsin(pi/6)" "=" "P_1P_3" "=" "sqrt(26)/2$

So $r = \frac{\sqrt{26}}{2 sin (\frac{π}{6})}$ $" "r = sqrt(26)/(2sin(pi/6))$

From which you can derive the length of arc

Points (8 ,5 )(8,5)(8 ,5 ) and (3 ,4 )(3,4)(3 ,4 ) are ( pi)/3 π3( pi)/3 radians apart on a circle. What is the shortest arc length between the points?