# Finding a tangent vector from a given point and circle

Hi all

Im working on some AI navigation, and I would like the vehicle to aim up for the tangent *b* (reference picture at the bottom). I got most of the stuff figured out at the moment (thanks to this great answer), but I'm still struggling with the maths in C#.

I have the point B, the direction of vector w, the length shouldn't matter. I also have point A, and the radius of the circle. What I'm missing is the point E, which is the intersecting point between the tangent of the circle, and the circle itself, and the direction of vector *b*.

Approximations are also alright, if they grant a performance boost - I'm not looking for accuracy, just a decent behaving ai :)

All help is appreciated!

**Answer** by elenzil
·
Mar 29 at 07:21 PM

oh hey, i know this.

core routine:

```
// this approach is more geometrical and less algebraic than approach 1,
// and far more stable. thanks to Mike Plotz for suggesting this direction.
bool CircleTangents_2(Vector2 center, float r, Vector2 p, ref Vector2 tanPosA, ref Vector2 tanPosB) {
p -= center;
float P = p.magnitude;
// if p is inside the circle, there ain't no tangents.
if (P <= r) {
return false;
}
float a = r * r / P;
float q = r * (float)System.Math.Sqrt((P * P) - (r * r)) / P;
Vector2 pN = p / P;
Vector2 pNP = new Vector2(-pN.y, pN.x);
Vector2 va = pN * a;
tanPosA = va + pNP * q;
tanPosB = va - pNP * q;
tanPosA += center;
tanPosB += center;
return true;
}
```

and finally a picture:

### Your answer

### Welcome to Unity Answers

The best place to ask and answer questions about development with Unity.

To help users navigate the site we have posted a site navigation guide.

If you are a new user to Unity Answers, check out our FAQ for more information.

Make sure to check out our Knowledge Base for commonly asked Unity questions.

If you are a moderator, see our Moderator Guidelines page.

We are making improvements to UA, see the list of changes.

### Follow this Question

### Related Questions

Meaning of inWeight and outWeight in Keyframe, or recalculate tangents from sampling 0 Answers

how to calculate the angle between two vectors? 6 Answers

Non physics determinism of floating point math across platforms 1 Answer

TransformPoint/Direction/Vector Equation? 0 Answers

Extending tangent length 0 Answers