Help me get angle
Author
Hi! I need help with this problem i have, cant think out any rule in this situation... Basicaly i have one point, and a circle with given radius and i need to get angle to create two rays that each touch circle in one point. I made this picture to explain more:
If the distance from your point to the center of the circle is D, and the radius of the circle is R, then you'd want the arcsin of R/D.
Author
Thanks, im stunned by this simple mathematical formula you gave, where did you get that? I want to be able to come up with something like that to, can you suggest any books or sites? ;D
Back to point - I can construct points i need by using that angle...(i could construct new line from line that goes from point to circle center and rotate it by angle, then finding whats the closest point on that new line to circle center)
But as it involves vector rotating and that means quite a bit of heavy instructions im thinking there should be an easier way to do this... So there is my question (new one, again, yeah..) - If i would create imaginary circle whose center is in middle of line CircleCenter -> Point, and radius is D/2, would that new circle intersect with old circle in points i need? In that case ill need just calculate circle-circle intersection points... I might be wrong thought.
Edit: And it seems that circle x circle approach will do for me in this case =]
[Edited by - Semei on June 19, 2009 11:28:06 PM]
Back to point - I can construct points i need by using that angle...(i could construct new line from line that goes from point to circle center and rotate it by angle, then finding whats the closest point on that new line to circle center)
But as it involves vector rotating and that means quite a bit of heavy instructions im thinking there should be an easier way to do this... So there is my question (new one, again, yeah..) - If i would create imaginary circle whose center is in middle of line CircleCenter -> Point, and radius is D/2, would that new circle intersect with old circle in points i need? In that case ill need just calculate circle-circle intersection points... I might be wrong thought.
Edit: And it seems that circle x circle approach will do for me in this case =]
[Edited by - Semei on June 19, 2009 11:28:06 PM]
let's call your point 'O', the circle centre 'C', the circle radius 'r', and the intersection point 'A' and 'B' (the pink points on the circle).
the distance from C to A is r (A is on the circle).
the line (OA) is tangent to the circle. That means that (OA) is perpendicular to (CA) (basic circle properties).
(OAC) form a right-angled triangle, the angle at point A is 90 degrees.
From the properties of a right angle triangle,
sin (angle(AC, OC)) = |AC| / |OC|
angle(AC, OA) = arcsin(|AC| / |OC|) = arcsin(r / |OC|).
That's trigonometry 101 [smile].
It's a bit early in the morning, I don't quite get your second question ;)
the distance from C to A is r (A is on the circle).
the line (OA) is tangent to the circle. That means that (OA) is perpendicular to (CA) (basic circle properties).
(OAC) form a right-angled triangle, the angle at point A is 90 degrees.
From the properties of a right angle triangle,
sin (angle(AC, OC)) = |AC| / |OC|
angle(AC, OA) = arcsin(|AC| / |OC|) = arcsin(r / |OC|).
That's trigonometry 101 [smile].
It's a bit early in the morning, I don't quite get your second question ;)
Quote:
If i would create imaginary circle whose center is in middle of line CircleCenter -> Point, and radius is D/2, would that new circle intersect with old circle in points i need?
Yes.
http://en.wikipedia.org/wiki/Thales'_theorem
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