If I understand your goal you want to create a fillet between 2 straight lines such that the fillet arc passes through a specified point "p" that is not on either of the two lines. The radius "r" of the arc is unknown.
If so, you can draw the angle bisector to the two lines. There are actually two angle bisectors but we can assume the one to use is implied by the bounds of the lines. The center of the fillet is on this line but where? We know that arc center is a distance r from either line (measured perpendicular to the line) and from the point p.
You can guess a point p1 on the angle bisector and then determine r and the distance s (the distance from p1 to p). If s is less than r determine a new point p2 further out from the intersection of the two lines. and recalculate r and s. Repeat until r and s are equal within a given tolerance. You can modify the guessing process to speed convergence to a solution.