## Find a tangent point on circle?

See the question and my original answer on StackOverflowHere is a C# solution (it can be easily adapted to other languages) that doesn't use trigonometric functions, only geometric construction.

You can see a living representation here (P, C and radius can be moved): https://www.desmos.com/calculator/ifzt2nzyl9

```
public static double[] GetTangentPoints(
double px,
double py,
double cx,
double cy,
double radius)
{
var points = new double[4];
var dx = cx - px;
var dy = cy - py;
if (dx == 0 && dy == 0)
return null; // no solution
// PC is distance between P and C, pc2 is PC^2
var pc2 = dx * dx + dy * dy;
var pc = Math.Sqrt(pc2);
if (pc < radius)
return null; // no solution
// R is radius of circle centered in P, r2 is R^2
var r2 = pc2 - radius * radius;
// d is the P => X0 distance (demonstration is here https://mathworld.wolfram.com/Circle-CircleIntersection.html where PC is named 'd' in there)
var d = r2 / pc;
// h is the X0 => X1 (and X0 => X2) distance
var h = Math.Sqrt(r2 - d * d);
// first tangent point
points[0] = px + (dx * d - dy * h) / pc;
points[1] = py + (dy * d + dx * h) / pc;
// second tangent point
points[2] = px + (dx * d + dy * h) / pc;
points[3] = py + (dy * d - dx * h) / pc;
return points;
}
```