A circle's center is at $(2, 7)$ $(2 ,7 )$ and it passes through $(6, 4)$ $(6 ,4 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

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A circle's center is at $(2, 7)$ $(2 ,7 )$ and it passes through $(6, 4)$ $(6 ,4 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

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Answer 1 · 2018-05-15T13:51:16

arc length $= \frac{550}{21}$ $=550/21$ units.

Explanation:

Let $C (2, 7) and P (6, 4)$ $C(2,7) and P(6,4)$ be the center and passing point of the circle respectively.

$\to$ $rarr$ Radius of the circle $= C P = \sqrt{{(6 - 2)}^{2} + {(4 - 7)}^{2}} = 5 u n i t s$ $=CP=sqrt((6-2)^2+(4-7)^2)=5 units$

$\to θ = \frac{l}{r}$ $rarrtheta=l/r$ where $θ, l and r$ $theta,l and r$ are the central angle, arc length and radius of the circle respectively.

$\to \frac{5 π}{3} = \frac{l}{5}$ $rarr(5pi)/3=l/5$

$\to l = \frac{25 π}{3} = \frac{25 \cdot \frac{22}{7}}{3} = \frac{25 \cdot 22}{7 \cdot 3} = \frac{550}{21} u n i t s$ $rarrl=(25pi)/3=(25*22/7)/3=(25*22)/(7*3)=550/21 units$

So, the arc length is $\frac{550}{21}$ $550/21$ units.

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A circle's center is at $(2, 7)$ $(2 ,7 )$ and it passes through $(6, 4)$ $(6 ,4 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

1 Answer

Explanation:

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