about angles...

[paper thistle]

Can we say anything about Ao1E and Ao2E angles? If we know x and y, what can we say? x is the radius of the circle with center o1. and y is the radius of the circle centered on o2.

[pallid monolith]

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[oblique briar]

If you know either BC or O1O2, you should be able to find anything here.

[paper thistle]

We don't know either of them.

[oblique briar]

Do you only know x and y?

[paper thistle]

yep

[oblique briar]

Then there isn't enough data. After all, we can move the circles horizontally without changing x or y.

[paper thistle]

Are you sure? I only have this much data.

[oblique briar]

Well, yeah. I mean, we don't have a parameter here that fixes the distance between the circles, so they can be anywhere relative to each other horizontally.

[paper thistle]

So what can you say about the lengths AB and AC?

[oblique briar]

I recommend taking BC or O1O2 as the third parameter.

[oblique briar]

Again, not enough data.

Points A and E might not even exist.

[paper thistle]

Let's think like this. Let everything be as in the image I sent you. None of them are moving.

[oblique briar]

Then either BC or O1O2 must also be given.

Hold on, let me demostrate what I mean.

[paper thistle]

I only have x and y values. Also the photo above.

This is the original photo.

[oblique briar]

Hold on, almost done.

[paper thistle]

okay

Are you still there? @oblique briar

[oblique briar]

Yeah. Sorry, Geogebra's gif export takes a while. Here you go.

Here BC = l.

As you can see, we can change l without changing x or y. This, of course, changes the entire configuration.

So, just knowing x and y isn't enough to say anything.

[paper thistle]

Can you send me the link, please?

[oblique briar]

Well, I can send you the file. Here you go.

[paper thistle]

Thank you @oblique briar .

[brisk wren]

@paper thistle has given 1 rep to @oblique briar

[oblique briar]

You're welcome!

[fallow tide]

We can say that A, O_1, B, O_2 are the vertices of a kite.

[paper thistle]

so?

[fallow tide]

So, what do we know about kites?

[paper thistle]

nothing :)

[fallow tide]

...what's the definition of a kite?

[paper thistle]

hmm, If I draw a line from o1 to o2 it bisects the angle. am i right?

[fallow tide]

...no, that is not the definition of a kite.

It's a correct inference, but it's not correct as the answer to the question I asked.

Well. A correct inference depending on which angle "the angle" is.

[paper thistle]

Yes, I'm sorry I couldn't answer your question fully. For a moment I thought I had solved the question.

[fallow tide]

I'm pretty sure LordDarpinger is correct that we can't determine the measures of the angles or the lengths of anything because they're not sufficiently fixed, but we can still determine the relationships we would use to determine those things if they were fixed.

[paper thistle]

Thank you. @fallow tide