A circle has a center at (3,5). The point (3,8) is on the circle. What is the circumference of the circle to the nearest tenth of a unit?

The correct answer is 18.8 units

To find the circumference of a circle, we need to use the formula:

Circumference = 2 * π * r

Where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

Since the point (3,8) is on the circle, we can determine the radius of the circle by finding the distance between the center of the circle (3,5) and the point (3,8).

To find the distance between two points (x1, y1) and (x2, y2), we can use the distance formula:

Distance = sqrt((x2-x1)^2 + (y2-y1)^2)

In this case, the distance between (3,5) and (3,8) is:

Distance = sqrt((3-3)^2 + (8-5)^2)
= sqrt(0^2 + 3^2)
= sqrt(9)
= 3

So the radius of the circle is 3 units.

Now, we can plug this radius value into the circumference formula:

Circumference = 2 * π * r
= 2 * 3.14159 * 3
= 6.28318 * 3
= 18.84954

Rounded to the nearest tenth, the circumference of the circle is approximately 18.8 units.

I meant to say:

in a vertical line
(early morning senior moment)

radius = 3

(easy to see since the given point and the centre lie in a horizontal line)

C = 2πr = 6π units