A circle's center is at $(9, 3)$ $(9 ,3 )$ and it passes through $(2, 6)$ $(2 ,6 )$ . What is the length of an arc covering $\frac{2 π}{3}$ $(2pi ) /3$ radians on the circle?

Question

A circle's center is at $(9, 3)$ $(9 ,3 )$ and it passes through $(2, 6)$ $(2 ,6 )$ . What is the length of an arc covering $\frac{2 π}{3}$ $(2pi ) /3$ radians on the circle?

1 Answer

Impact of this question

1925 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-03T13:16:49

$\frac{2 π \sqrt{58}}{3} \approx 15.95043789$ $color(blue)((2pisqrt(58))/3~~15.95043789)$

Explanation:

Arc length is given by:

$r θ$ $rtheta$

Where $θ$ $theta$ is measured in radians.

We first need to find the radius of the given circle. Since the distance from the centre of a circle to any point on its circumference is the radius, we find the distance from:

$(2, 6)$ $(2,6)$ to $(9, 3)$ $(9,3)$

Using the distance formula:

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$| r | = \sqrt{{(9 - 2)}^{2} + {(3 - 6)}^{2}} = \sqrt{58}$ $|r|=sqrt((9-2)^2+(3-6)^2)=sqrt(58)$

Using $r θ$ $rtheta$

$\sqrt{58} (\frac{2 π}{3}) = \frac{2 π \sqrt{58}}{3} \approx 15.95043789$ $sqrt(58)((2pi)/3)=(2pisqrt(58))/3~~15.95043789$

Science

Math

Humanities

... and beyond

A circle's center is at $(9, 3)$ $(9 ,3 )$ and it passes through $(2, 6)$ $(2 ,6 )$ . What is the length of an arc covering $\frac{2 π}{3}$ $(2pi ) /3$ radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle's center is at (9,3)(9 ,3 ) and it passes through (2,6)(2 ,6 ). What is the length of an arc covering 2π3(2pi ) /3 radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

A circle's center is at $(9, 3)$ $(9 ,3 )$ and it passes through $(2, 6)$ $(2 ,6 )$ . What is the length of an arc covering $\frac{2 π}{3}$ $(2pi ) /3$ radians on the circle?