You use the definite article "the" when you are referring to something specific that would not otherwise be recognised as such. For example, you might say "the car" when referring to a specific car, because there are many cars; but if you had already identified a specific car by some other means there would be no need for the definite article. You wouldn't say "the John's car"; you would just say "John's car", presuming that your audience knows who John is.
In your first two examples, you refer to specific drawings by labelling them "Drawing A" and "Drawing B". As this naming convention already makes it clear which is which, there is no need for the definite article.
The correct renditions are:
Point A is equidistant from lines B and C.
I find drawing A nicer than drawing B.
In your final example, it depends on whether you are using the three-word phrase "Samtec Text Editor" as the complete name for a product. If that is a recognised name, then you are naming a specific product and there is no need for the definite article:
Samtec Text Editor™ is faster than competing products.
However, if that is not the name of the product and you are simply calling it "a text editor" to show that it is one of many text editors, then the definite article may be required to differentiate it from the other text editors you refer to:
The Samtec text editor is faster than the other text editors.
An alternative way of phrasing this without the definite article might be to use the possessive:
Samtec's text editor is faster than the others.
This identifies it as being the text editor belonging to Samtec, whatever the actual name of the product is.