# Thread: Finding a point on a circle, given only anothe point, the radius, and the arc length

1. ## Finding a point on a circle, given only anothe point, the radius, and the arc length

Hi all,
I'm trying to find a point on a circle given only an existing point on the circle (2,3), the radius, and the arc length between the points.
In other words I don't have the centre point co-ordinates.

Is this possible?

2. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Originally Posted by davrosg
Hi all,
I'm trying to find a point on a circle given only an existing point on the circle (2,3), the radius, and the arc length between the points.
In other words I don't have the centre point co-ordinates.
I don't think that you wrote what you are actually thinking.
If you use the point $(2,3)$ a center of a circle with radius $10$, then any point on that circle is a centre of another circle containing $(2,3)$

3. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Sorry, don't know what you mean.
I'm looking for the coordinates of the blue point on the circle. I know another point (red dot) on the circle (2,3), the radius, and the arclength between the two points. I do not know the position of the centre of the circle

4. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

The co-ordinates of your blue point cannot be determined with the data given. There are an infinite number of different circles that have radius 10 and contain the point (2, 3). Any point on the circle using (2, 3) as the center with a radius of 10 is the potential center of a circle with radius 10 containing (2, 3). You have drawn just one of those possible circles, but have not told us how you determined it to be the correct circle.

Even if you knew the co-ordinates of the center, you would get two possible blue points, not a unique one.

5. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Originally Posted by davrosg
Sorry, don't know what you mean.
I'm looking for the coordinates of the blue point on the circle. I know another point (red dot) on the circle (2,3), the radius, and the arclength between the two points. I do not know the position of the centre of the circle
see attached diagram. same situation in the second circle ... known arc length, s, radius, $r=10$, and one fixed point on the circle, $(2,3)$

what do you think?

6. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Step1 would be to calculate central angle:

C = circle center, R = Red point, B = Blue point
u = central angleBCR (?)
a = arc length (given)
p = pi

u = 180a / (pr)

If r = 10 and arc = 9, you'll get u = ~51.57 degrees

Note:
sorry Skeeter; didn't see your post;
to OP: I'll leave the rest with Skeeter: he's beyond me...

7. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Several people answered your question while I was making the following drawing. However, it might help:

8. ## Re: Finding a point on a circle, given only anothe point, the radius, and the arc len

Originally Posted by davrosg
I'm looking for the coordinates of the blue point on the circle. I know another point (red dot) on the circle (2,3), the radius, and the arclength between the two points. I do not know the position of the centre of the circle