How to find the coordinates of the line d, directed along the bisector of the angle between two lines, provided that the length of the biss of the line c is specified from the keyboard?

Question

Mathematics

We have coordinates a(3,4) b(5,4) c(5,7) and the length of the bisector, let's say 4, we need to find the coordinates where the bisector will fall

Answer 1

As I understand it, the task is as follows. There is an angle given by a vertex and two points on the sides. Find where the bisector of length 4 will fall.
1. From the coordinates of the corner vertex and points on its sides, get the side vectors.
2. Bring side vectors to a single length (for example, divide by length).
3. Their arithmetic mean is a vector bisector. If you get a zero vector, the side vectors look at 180 °, and it is not clear in which direction to consider our bisector.
4. Bring the bisector vector to the desired length (dividing by the real length and multiplying by the required one).
5. Calculate this vector from the top of the corner. The coordinate of the bisector of length 4, laid off from the point (3, 4), will be obtained.
Mathematics is not the best :)

Answer 2

tutata.ru/217 - above the "solve" button there is a link "solution example"