How to find the coordinate of a point that a line intersects?

Question

Mathematics

Hello!
Given three vertices of an arbitrary triangle ABC;
We know:
1) Coordinates of points A,B,C;
2) The lengths of the sides of triangle ABC;
3) One corner B;
4) QD length;
5) The length of the bisector BM;
6) Height length MF of triangle BMA;
The essence of the question is that I need to find the coordinate of the point of intersection of the line QD with the bisector BM. I spent a lot of time on this, I didn’t manage to google anything.

Answer 1

find the coordinate of the point of intersection of the line QD with the bisector BM

If only its length is known about QD, then there will be an infinite number of solutions.
If the angle BDQ is also known (for some reason it is drawn 90 degrees in the figure), then:
1. the formula of the straight line BA - from the coordinates B and A
2. the formula of the straight line BM - from the formula of the straight line BA rotated by the angle QBD
3. the length of BQ - from the sine of angle QBD and length QD
4. coordinates Q - from coordinates B, line formula BM and length BQ
However, if you prefer to google rather than open a school geometry textbook, I have doubts that you can calculate this even from my chewed algorithm.

Answer 2

I have a triple in mathematics, but I suspect that we should smoke about the similarity of triangles.

Answer 3

And what does the tag "algorithms" have to do with it, if it's pure geometry?
Maybe we will start looking in algorithms for solving equations like ax+b=0?

Answer 4

Two similar right triangles with known sides. Plug it into the formula and you're done.