I know this is a simple question but I cant find the name for this.
(For a figure go to the bottom of the question)
I know that for similar triangles $\Delta ABC$ $\Delta A'B'C'$ I can divide any two similar sides and get the scale factor $K$
The scale, of course, changes for different similar triangles. However, if I where to do some algebra.
I get to some constant $m$ that does not change between any similar triangles.
I also noticed that has some kind of relationship with the law of sines. I want to know:
1)what is the name of this constant or how can I search for it (could not find it).
2)If there is an analogus euclid element's proposition about it.
Here is an example on geogebra. If you drag the "drag me" point you are generating a diferent triangle $A'B'C'$ similar to $ABC$ and you can see how $K$ changes but $m$ stays the same for both triangles independently of their difference in size https://www.geogebra.org/classic/kbwzynd6