Maria's Puzzle Book Reloaded [Puzzle 26]

So yeah, this is a continuation of this thread, as I’m changing the rules though I’m making a new thread. As I have far too many puzzles to make a new topic for each one, I’ll instead post a new one here once an old one has been solved. Unlike for picto’s puzzle, number crunching is required for some puzzles, but just like picto’s puzzle, they are all solvable with the knowledge you got in school. Also, I honestly don’t feel like continuing to get rid of the christmas theme these puzzles had originally, so I hope you don’t mind.

You can always ask questions for each puzzle, and it’s sufficient if you just bold your questions, no need to use pink or anything like that (of course, you can use pink if you want). I won’t guarantee to answer every question, though.

These puzzles also come with a difficulty rating, with 1 being the easiest and 6 being the hardest.

Other than that, I’ll use this OP to quickly link to each puzzle, since this topic has the potential to be quite big once some puzzles have been solved. (Puzzles 1 to 20 are all in the old thread)

Links to Puzzles

Puzzles 1 to 5
Puzzles 6 to 10
Puzzles 11 to 15
Puzzles 16 to 20
Puzzle 21
Puzzle 22
Puzzle 23
Puzzle 24
Usagi’s Guest Puzzle
midsummer’s Guest Puzzle
Puzzle 25
Puzzle 26

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Does this manger stand inside the triangle, outside the triangle, or on one of the sides of the triangle?

I’m not at home right now but I think it’s definitely not on one of the side because that would make 3 diameters intersect and that would be just a point not triangle
I drew triangle first and extended chords infinitely and then just placed circle on top
I found radius of a circle r = (chord lenght^2/(4height of a triangle) + height of a triangle)/2 = around 6,12 so 12,24 in diameter
I checked using ruler and also drew it on the paper and I guess it’s inside

I’m curious how you got to this formula.

It was one of the theorems in our geometry textbook and I had it in my school notebook, lol I wanted to throw it away.

Okay, the algebra is correct there, but following your picture, h is not the height of the triangle, but the remaining part of the radius after subtracting the height (since the height of the triangle in that image is labeled with “r-h”). Besides, you don’t know h, so how did you calculate that? What did you insert for h?

Omg I’m stupid. I inserted the height of the triangle but it still kinda fits lol

See I want it exactly fitting, otherwise you might be wrong, you don’t know. In fact, check the lengths of the chords in your construction in the first picture, do they have the same length?


I did it with a more precise tool that allows to place in cm, so it does fit

So for your second construction, measuring with a ruler myself, the chord labeled 4 is 6.7 cm long. The chord labeled 5 is 8 cm long. The chord labeled 7 is 8.5 cm long. Therefore, your construction there can’t be right.

To everyone else reading this, this means this puzzle isn’t solved yet, so feel free to chime in if you have any ideas yourself.

It’s probably because it was zoomed in but whatever maybe we have to actually explain it mathematically but thats boring

It has nothing to do with any zooming, your second construction is definitely wrong.

Is first one too?

man i will have no part in these circle theorems and stuff, i want out

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Yes, the first one is wrong as well.

Are the angles of triangle


Well atleast I got that right.
I just tried to make it again and only 1 side didnt fit a little :mii:

Ok I did height of the triangle but I’m not sure if I can calculate it that way and found the sides with sinuses and pythagorean formulas. Is that correct or I’m heading the wrong way again
I guess to draw circle really precise we have to find the length of a line before and after sides of our triangle

Well the thing is I myself don’t know all the lengths and stuff, as this puzzle can be solved without calculating anything. It might be possible to figure out all the lengths through calculation and then construct the entire thing, which is why I didn’t shut down this approach. But perhaps this red gives others some new ideas, who knows.