Finding a second point on a circle

[chuckrussell]

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?

Attached is a picture diagramming my dilemma

 

[tiny-tim]

welcome to pf!

hi chuckrussell! welcome to pf!

hint: dot product

 

[chuckrussell]

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?

 

[AlephZero]

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).

 

[blue_raver22]

.
Hello there,

Thank you for reaching out with your question about finding a second point on a circle. I understand the importance of accurately solving problems and the frustration that can come with a lack of available information.

To find a second point on a circle at a given angle, you can use the trigonometric functions sine and cosine. By using the coordinates of the center point and the radius of the circle, you can calculate the coordinates of the second point using the following formulas:

x' = h + r*cos(a)
y' = k + r*sin(a)

Where a is the angle you are looking for, and x' and y' are the coordinates of the second point on the circle.

I hope this helps you in your search for a solution. If you have any further questions or need clarification, please don't hesitate to reach out. Best of luck in your research!

Sincerely,