How to calculate points of Chord

Question

Hi,

I need to calculate a chord`s starting and ending point, now I have the starting point which lies on the circumfrence of the circle and I also have the angle between starting point and ending point, but I cannot seem to find a way to determine the end of point of chord as it should lie on the circumfrence , I also have the centre and radius of circle, the methods I have looked over the internet all give chord length. So i in short I need to find the other end of a chord when one point and the angle between both points is given, any idea of links would be appreciated

thanks Imran

Answer 1

The arbitrary point on the circle with center (X0,Y0) and radius R has coordinates

x = Xo+R*cos(a)
y = Y0+R*sin(a), 0<=a<2*Pi 

knowing X,Y,X0,Y0 and R you can easily find angle a:

a = acos((x-X0)/R) (may be + Pi depending on sign of the y-Y0).

Then you can calculate the angle for the second chord endpoint (you'll have two solutions actually) - a+angle and a-angle. Then put angle you got into circle equation and you'll get your required points coordinates.