Let be the intersect points between the line and the circle. Then .
The line AO has the slope and the line BO has the slope
The tangent of the acute angle between the two lines is
Replace and :
The coordinates of A and B are the solutions of the system formed by the equation of the line and equation of the circle.
Replace y in the equation of the circle and we have:
are the roots of the quadratic and we have
Replace in (1):
Now replace and .
The positive root is .
Square both members: