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January 25th, 2013, 10:39 AM  #1 
Newbie Joined: Jan 2013 Posts: 3 Thanks: 0  Calculating circle's coordinates using radius and rotation?
Image here If I know radius of the circle, O's coords and alpha, can I calculate B's coords? I have painted as red that, what, I think, might be helpful. Thank you in advance. 
January 25th, 2013, 10:55 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Calculating circle's coordinates using radius and rotati
Let be the coordinates of O and be the radius of the circle, then we may write the coordinates of B as: 
January 25th, 2013, 11:41 AM  #3 
Newbie Joined: Jan 2013 Posts: 3 Thanks: 0  Re: Calculating circle's coordinates using radius and rotati
Many thanks I would also like to ask... is it possible to calculate alpha from B's (and O's) coordinates and ? 
January 25th, 2013, 11:46 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Calculating circle's coordinates using radius and rotati
Yes, you would have to use the inverse sine and cosine functions along with some attention to which quadrant the relative position of B to O places the angle .

January 26th, 2013, 12:29 AM  #5  
Newbie Joined: Jan 2013 Posts: 3 Thanks: 0  Re: Calculating circle's coordinates using radius and rotati Quote:
Can You write whole formula?  
January 26th, 2013, 07:40 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Calculating circle's coordinates using radius and rotati
It would really be an algorithm rather than a formula. You would have to use conditional statements based on B's relation to O to determine the quadrant of .

February 19th, 2013, 08:58 PM  #7 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Calculating circle's coordinates using radius and rotati
You know the radius of the circle. That means you can write an equation for that circle. You know the angle of line OB. That means you know the slope, by tangent. If know know the slope of a line and that it intersects the center of the circle, you can write an equation for the line. Solve for x and y as the interception of the circle and the line. 

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calculating, circle, coordinates, radius, rotation 
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