I'm passing through "geometric constructions" topic and a lot of exercises have the same question in the end of their conditions:
How many solutions does the exercise have ?
For example, let's assume that I found a required triangle from the next exercise:
Construct a triangle by two altitudes and an angle, from the top of which one of the given altitudes is drawn. Also write, how many solutions the exercise has.
How do I even know how many solutions can an exercise has, when I've already drawn a required figure ?
How to know that, what is the algorithm of finding a possible solutions quantity ?