Calculating intersection point of two tangents on one circle?

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 + you * (CA. Y, -CA.

X) = (A. X + you * CA. Y, A.

Y - you * 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.

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 + you * (CA.

Y, -CA. X) = (A. X + you * CA.

Y, A. Y - you * 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.

Awesome, that's just what I needed, thanks :D! – Conros Jun 26 at 16:04.

The answer by Peter Alexander assumes that you know the center of the circle, which is not obvious from your figure

. 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.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.