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 $A.$

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

If the pairs of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ bisect the angles between each other, then which of the following is correct?

If $A\left(x_1,y_1\right), B\left(x_2,y_2\right), C\left(x_3,y_3\right)$ are the vertices of the triangle then find the equation of angle bisector through $A,$ where $a,b,c$ units are the lengths of the sides opposite to the vertices $A,B,C$ respectively.
 

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

If $r\left(1-m^2\right)+m\left(p-q\right)=0,$then find the bisector of angle between the lines represented by the equation $p{x}^2-2rxy+q{y}^2=0,$ (where $m$ is slope of line $y=\mathit{mx}$)

The locus of the point $P$ which is equidistant from $3x+4y+5=0$ and $9x+12y+7=0$ is

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

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