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

Use the x,y coordinates of the intersecting equations (the one of the circle and the one of the line). That's the point.

If you have only one end point from which to draw the line you'll get two different points, as there will be two different tangent lines, one up and one down.