I have two lines:
$$a_1x+b_1y=c_1 \tag{1}$$ $$a_2x+b_2y=c_2 \tag{2}$$
I know that the two angle bisectors are expressed by
$$\frac{a_{1}x+b_{1}y-c_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}}=\pm \frac{a_{2}x+b_{2}y-c_{2}}{\sqrt{a_{2}^{2}+b_{2}^{2}}}\tag{3}$$
Is there any link between the sign of RHS in $(3)$ and the bisector of the smallest (biggest) angle?