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 :

, (1)

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 .

Let .

Then

The positive root is .

.

Square both members: