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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 ?

curioushuman
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  • If you have a textbook to share with us from which you're taking these exercises, that's be helpful to attach (especially if it's an online PDF). If you just know the name, mentioning it would be useful if someone can retrieve the exercises. – Sarvesh Ravichandran Iyer Jul 06 '22 at 06:32
  • Sure I would attach .pdf, but the textbook is on the Ukrainian language, and I don't think you would understand anything. Also the exercises online translation is very inaccurate, so I did my best. – curioushuman Jul 06 '22 at 12:39
  • Oh, I see, this is unfortunate (although, thank you for translating the exercise). I think you should attach it just in case some Ukrainian happens to walk across. I can read the script, but I'll have to see how many words I can actually understand. But I have some idea of what you mean : sometimes, there can be more than one solution, so the question is basically "how many solutions there can be" to some exercise. Actually, thinking about it, your question is clear. Just attach the Ukrainian source, I'll look through it with some effort – Sarvesh Ravichandran Iyer Jul 06 '22 at 12:42
  • This question is more difficult than just drawing the figure : the figure could be drawn in a way different to how you have drawn it, so there could b more than one solution. This question is actually not very easy, so it would be good if it got some nice attention. – Sarvesh Ravichandran Iyer Jul 06 '22 at 12:45
  • Here exercise 610. – curioushuman Jul 06 '22 at 18:11

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