A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(8, 3)$ $(8 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $( pi ) /3$ radians on the circle?

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Answer 1 · 2016-08-14T07:46:34

Given that coordinate of the center of a circle is $(2, 4)$ $(2,4)$ and the coordinate of another point on it is $(8, 3)$ $(8,3)$ .

$So its radius (r) = \sqrt{{(8 - 2)}^{2} + {(3 - 4)}^{2}} = \sqrt{37}$ $"So its radius"(r)=sqrt((8-2)^2+(3-4)^2)=sqrt37$

So length of the arc (S) covering $\frac{π}{3}$ $pi/3$ radian on circle will be

$S = r \times angle = \sqrt{37} \times \frac{π}{3} = 6.37 u n i t$ $S=rxx"angle"=sqrt37xxpi/3=6.37unit$

A circle's center is at (2,4)(2 ,4 ) and it passes through (8,3)(8 ,3 ). What is the length of an arc covering π3( pi ) /3 radians on the circle?