Calculating intersection point of two tangents on one circle?

I tried using a raycasting-style function to do it but开发者_如何学Python can't get any maintainable results. I'm trying to calculate the intersection between two tangents on one circle. This picture should help explain:

I've googled + searched stackoverflow about this problem but can't find anything similar to this problem. Any help?

Well, if your variables are:

C = (cx, cy) - Circle center
A = (x1, y1) - Tangent point 1
B = (x2, y2) - Tangent point 2

The lines from the circle center to the two points A and B are CA = A - C and CB = B - C respectively.

You know that a tangent is perpendicular to the line from the center. In 2D, to get a line perpendicular to a vector (x, y) you just take (y, -x) (or (-y, x))

So your two (parametric) tangent lines are:

L1(u) = A + u * (CA.y, -CA.x)
      = (A.x + u * CA.y, A.y - u * CA.x)

L2(v) = B + v * (CB.y, -CB.x)
      = (B.x + v * CB.y, B.x - v * CB.x)

Then to calculate the intersection of two lines you just need to use standard intersection tests.

The answer by Peter Alexander assumes that you know the center of the circle, which is not obvious from your figure http://oi54.tinypic.com/e6y62f.jpg. Here is a solution without knowing the center:

The point C (in your figure) is the intersection of the tangent at A(x, y) with the line L perpendicular to AB, cutting AB into halves. A parametric equation for the line L can be derived as follows:

The middle point of AB is M = ((x+x2)/2, (y+y2)/2), where B(x2, y2). The vector perpendicular to AB is N = (y2-y, x-x2). The vector equation of the line L is hence L(t) = M + t N, where t is a real number.