Angle Bisectors

Given vertices $A(1, 1), B(4,-2) \& C(5, 5)$of a triangle, find the equation of the perpendicular dropped from $C$ to the interior bisector of the angle $A.$

Find the equation of the bisector of the obtuse angle between the lines $3x-4y+7=0$ and $12x+5y-2=0$.

Cotyledons are also called-

The equation of  bisector of the acute angle formed between the lines $4x-3y+7=0$ and $3x-4y+14=0$ has the equation is 

Equation of angle bisector between the lines $3x+4y-7=0$ and $12x+5y+17=0$ are

The equation of the bisector of the angle between the lines $x+2y-11=0, 3x-6y-5=0$ which contains the point $\left(1,3\right)$ is

Equation of angle bisectors between $x$ and $y$ - axes are

The equation of the line which bisects the obtuse angle between the lines $x-2y+4=0$ and $4x-3y+2=0$ , is

The equation of the bisector of the acute angle between the lines $3x-4y+7=0$ and $12x+5y-2=0$ is

The equation of the bisectors of the angles between the lines $\left|x\right|=\left|y\right|$ are

Equation of angle bisectors between the lines $3x+4y-7=0$ and $12x+5y+17=0$ are

Let $P=\left(-1,0\right), Q=\left(0,0\right)$ and $R=\left(3, 3\sqrt{3}\right)$ be three points. Then, the equations of the bisector of the angle $PQR$  is