Find a tangent point on circle?

Question

Given a line with first end point P(x1,y1) another end point is unknown, intersect with a circle that located at origin with radius R at only one point(tangent) T(x2,y2). An

Answer 1

All you need is in dmckee's answer, but if you care for some code check this implementation using Javascript and HTML canvas.

Full example: http://jsfiddle.net/zxqCw/1/

// find tangents
dx = cx - px;
dy = cy - py;
dd = Math.sqrt(dx * dx + dy * dy);
a = Math.asin(radius / dd);
b = Math.atan2(dy, dx);

t = b - a
ta = { x:radius * Math.sin(t), y:radius * -Math.cos(t) };

t = b + a
tb = { x:radius * -Math.sin(t), y:radius * Math.cos(t) };