We help IT Professionals succeed at work.

New podcast episode! Our very own Community Manager, Rob Jurd, gives his insight on the value of an online community. Listen Now!

x

# angle in a circle

on
812 Views
markww    Member since: 4/5/2007

Posted - 10/13/2007 2:19:29 PM
Hi,

I have a circle, I know its radius. I have a point on its edge. Is there anyway to figure out what angle in degrees that is?

|
------|----
/         |        \
P         |         \
|          |           |
----------O-------X--------
|          |           |
\         |         /
\------|---- /
|
|

yeah that's a fine ascii circle, so anyway, I'm interested in the angle formed between P, O, X. I know the coordinates of all 3, I just want to know the angle between them.

Thanks for any help

p.s. - the formatting keeps messing up the circle (not that it was that great to begin with, hope it's understandable)
Comment
Watch Question

## View Solution Only

Commented:
Unlock this solution and get a sample of our free trial.
(No credit card required)
CERTIFIED EXPERT
Most Valuable Expert 2014
Top Expert 2015

Commented:
in  general arccos( (X-O) dot (P-O) / (|X-O| * |P-O|) )

Commented:
Use your cordinates to determine the length of the intercepted arc between p and x. The angle in radians = the length of the arc / the length of the radius.  The formula found in my Trig book is omega = s / r.  Then convert radians to degrees with 2 pi radians = 360 degree (circumference of a circle).

I don't remember and not able to quickly find how to get the length of the arc segement.  Will let you know if I find out.  Please give details of the coordinates and other information you have about this problem.
CERTIFIED EXPERT
Most Valuable Expert 2014
Top Expert 2015

Commented:
You can find the arc from the cosine of the dot product
CERTIFIED EXPERT
Most Valuable Expert 2014
Top Expert 2015

Commented:
http://en.wikipedia.org/wiki/Dot_product#Geometric_interpretation
If you already know |a| = |b| = radius then you only need a ยท b
Unlock the solution to this question.