The equation of the bisector of the acute angle between the lines $2x - y + 4 = 0$ and $x - 2y - 1 = 0$ is

The vertices of a triangle are $A(1, 7)$,$B(-5, -1)$,and $C(-1, 2)$. Then,the equation of a bisector of the $\angle ABC$ is

Let $A(1,0)$, $B(2,-1)$, and $C(\frac{7}{3},\frac{4}{3})$ be three points. If the equation of the internal angle bisector of $\angle ABC$ is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is

Let the line $L_1 : x + 3 = 0$ intersect the lines $L_2 : x - y = 0$ and $L_3 : 3x + y = 0$ at the points $A$ and $B$, respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point $C$. Then $BC^2 : AC^2$ is equal to:

Let $B_1: 3x + 4y - 7 = 0$ and $B_2: 4x - 3y - 14 = 0$ be the angle bisectors of the angle between the lines $L_1 = 0$ and $L_2 = 0$. If $L_1$ passes through the point $(1, 2)$,then which of the following is true?

Let $P(-1, 0)$,$Q(0, 0)$,and $R(3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle $\angle PQR$ is: