A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(6, 6)$ $(6 ,6 )$ . What is the length of an arc covering $\frac{13 π}{12}$ $(13pi ) /12$ radians on the circle?

Question

A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(6, 6)$ $(6 ,6 )$ . What is the length of an arc covering $\frac{13 π}{12}$ $(13pi ) /12$ radians on the circle?

1 Answer

Impact of this question

2203 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-17T11:40:49

$19.845$ $19.845$

Explanation:

The radius of the circle is
$XXX r = \sqrt{{(6 - 3)}^{2} + {(6 - 1)}^{2}} = \sqrt{3^{2} + 5^{2}} = \sqrt{34}$ $color(white)("XXX")r=sqrt((6-3)^2+(6-1)^2) = sqrt(3^2+5^2) = sqrt(34)$

Since a circle has a circumference (arc length) of $2 r π$ $2rpi$
and an arc angle of $2 π$ $2pi$ :
$\frac{arc length}{arc angle} = \frac{2 r π}{2 π} = \frac{required arc length}{\frac{13 π}{12}}$ $("arc length")/("arc angle") = (2rpi)/(2pi) = ("required arc length")/((13pi)/12)$

$"required arc length"=(13pi)/12*(cancel(2)rcancel(pi))/(cancel(2)(cancelpi))=(13pir)/12$

$color(white)("XXXXXXXXXXX")=(13sqrt(34)pi)/12$

$color(white)("XXXXXXXXXXX")~~19.845$ (using a calculator)

Science

Math

Humanities

... and beyond

A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(6, 6)$ $(6 ,6 )$ . What is the length of an arc covering $\frac{13 π}{12}$ $(13pi ) /12$ radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle's center is at (3 ,1 )(3,1)(3 ,1 ) and it passes through (6 ,6 )(6,6)(6 ,6 ). What is the length of an arc covering (13pi ) /12 13π12(13pi ) /12 radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(6, 6)$ $(6 ,6 )$ . What is the length of an arc covering $\frac{13 π}{12}$ $(13pi ) /12$ radians on the circle?