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

1 Answer
Somebody N.
Jun 3, 2018

color(blue)((2pisqrt(58))/3~~15.95043789)

Explanation:

Arc length is given by:

rtheta

Where 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) to (9,3)

Using the distance formula:

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

|r|=sqrt((9-2)^2+(3-6)^2)=sqrt(58)

Using rtheta

sqrt(58)((2pi)/3)=(2pisqrt(58))/3~~15.95043789

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