Points $(6, 7)$ $(6 ,7 )$ and $(5, 5)$ $(5 ,5 )$ are $\frac{2 π}{3}$ $(2 pi)/3$ radians apart on a circle. What is the shortest arc length between the points?

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Points $(6, 7)$ $(6 ,7 )$ and $(5, 5)$ $(5 ,5 )$ are $\frac{2 π}{3}$ $(2 pi)/3$ radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2016-03-11T13:21:53

$= \frac{2 π \sqrt{5}}{3 \sqrt{3}}$ $=(2pisqrt5)/(3sqrt3)$

Explanation:

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AB = $\sqrt{{(6 - 5)}^{2} + {(7 - 5)}^{2}} = \sqrt{5}$ $sqrt((6-5)^2+(7-5)^2)=sqrt5$
Let radius of circle =r
$A B = A C + B C = r sin (\frac{π}{3}) + r sin (\frac{π}{3}) = 2 r sin (\frac{π}{3}) = \sqrt{3} r$ $AB=AC+BC=rsin(pi/3)+rsin(pi/3)=2rsin(pi/3)=sqrt3r$
$r = \frac{A B}{\sqrt{3}} = \frac{\sqrt{5}}{\sqrt{3}}$ $r=(AB)/(sqrt3)=sqrt5/(sqrt3)$

arc length = $r \times (2 \frac{π}{3}) = \frac{\sqrt{5}}{\sqrt{3}} \times (2 \frac{π}{3}) = \frac{2 π \sqrt{5}}{3 \sqrt{3}}$ $rxx(2pi/3)=sqrt5/(sqrt3)xx(2pi/3)=(2pisqrt5)/(3sqrt3)$

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Points $(6, 7)$ $(6 ,7 )$ and $(5, 5)$ $(5 ,5 )$ are $\frac{2 π}{3}$ $(2 pi)/3$ radians apart on a circle. What is the shortest arc length between the points?

1 Answer

Explanation:

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Science

Math

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Points (6,7)(6 ,7 ) and (5,5)(5 ,5 ) are 2π3(2 pi)/3 radians apart on a circle. What is the shortest arc length between the points?

1 Answer

Explanation:

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Points $(6, 7)$ $(6 ,7 )$ and $(5, 5)$ $(5 ,5 )$ are $\frac{2 π}{3}$ $(2 pi)/3$ radians apart on a circle. What is the shortest arc length between the points?