Finding a second point on a circle

  • Context: Undergrad 
  • Thread starter Thread starter chuckrussell
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Discussion Overview

The discussion revolves around finding a second point on a circle given a center point, radius, and an initial point on the circle, specifically at a certain angle from that point. The scope includes mathematical reasoning and potential formulas for solving the problem.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant seeks a method to find a point on a circle at a specific angle from a known point on the circle.
  • Another participant suggests using the dot product as a hint for the solution.
  • A third participant expresses frustration with the hint and requests a formula instead of just guidance.
  • A proposed method involves shifting the circle's center to the origin, using inverse tangent to find angles, applying sine and cosine to determine coordinates, and then shifting back to the original center.

Areas of Agreement / Disagreement

Participants have not reached a consensus on a specific formula or method, and there are differing levels of satisfaction with the guidance provided.

Contextual Notes

The discussion does not clarify the assumptions behind the proposed methods or the specific definitions of terms used, which may affect the applicability of the suggestions.

chuckrussell
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Hey, I have scoured the interned for an answer to this question, but so far my search has been uneventful.

Given a circle with center point (h,k), radius r, and a point on the circle (x,y), I need to find the point on the circle at angle a from (x,y).

Any thoughts?

attachment.php?attachmentid=32479&stc=1&d=1298482555.png

circle.png

Attached is a picture diagramming my dilemma
 
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welcome to pf!

hi chuckrussell! welcome to pf! :smile:

hint: dot product :wink:
 
Not going to lie, after searching for days on the topic, a hint is of almost no help. I appreciate it all the same, but could you perhaps just give me a formula to use?
 
One way is

Shift the center of the circle to the origin.
Find the angle of (x,y) from the center using the inverse tangent function
Find the angle of (i,j)
Find i and j using sin and cos
Shift the center back to (h,k).
 

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