Given a circle $x^2+y^2=r^2$ and a point P(x1,y1) outside of the circle. I can draw two tangents from P to the circle. I will call A and B the points where the tangents cross the circle. How can I show that the line that passes through A and B is defined by $x.x_1+y.y_1=r^2$?
The slope of the line is $-x_1/y_1$ because that line is perpendicular to the line that goes from (0,0) to (x1,y1).
How can I show that the intercept is $r^2/y_1$?