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?

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

A light ray is incident to a line mirror "L' along the line $3 \mathrm{x}-4 \mathrm{y}+5=0$ and is reflected along the line $5\mathrm{x}-$ $12 \mathrm{y}+19=0.$ The equation of line 'L' may be

Cotyledons are also called-

If $O$ is the origin and the line $OP$ of length $r$ makes an angle $\alpha$ with $x-$axis and lies in the $xz-$plane, then the co-ordinates of $P$ are-

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

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

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