# equation of angle bisector

by V0ODO0CH1LD
Tags: angle, bisector, equation
 P: 182 I've seen that if you have two lines: r = Ax + By + C = 0 and r = Dx + Ey + F = 0, you can say the equation of the line that is the angle bisector of r and s is given by: $$\frac{|Ax + By + C|}{\sqrt{A^2+B^2}}=\frac{|Dx + Ey + F|}{\sqrt{D^2+E^2}}.$$ Why is that? I would think to equate the distances from the angle bisector to each line. Is that what is happening here?
P: 39
 Quote by V0ODO0CH1LD I would think to equate the distances from the angle bisector to each line. Is that what is happening here?
Yes.
Angular bisector of an angle made by two lines is the locus of all points which are equidistant from both the lines. So that the equation of the bisector is given by equating the distances...

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