well, you can do this..
Let be a point on the circle such that the line connecting and is tangent to the circle.
so, using two-point form of a line, you get (line) with slope (slope 1)
note that if a line is tangent to a circle, then the line connecting the center of the circle and the point of tangency is perpendicular to .
the center of the circle if . so the slope of the line from this center of will be .
but this slope should be equal to the negative reciprocal of the slope of slope 1.
thus, .. -- (1)
(a,b) is on the circle, thus, it satisfies the equation of the circle..
and you have 2 equations and 2 unknowns...
you will get 2 ordered pairs and substitute it on the equation line to get the equation of the two lines..