An isosceles triangle is drawn around a circle. Prove that the

honestly that sounds like a proof that could be done just by deriving an equation for the area and doing some calculus for the minimum.
Ugly as fuck and maybe it turns out it you get some equations which are really hard to solve but there's a good chance it's pretty easy.

>>8655721
The hardest part here is deriving the equation.

>>8655714
Easy. Suppose it's not equilateral, then one of the bases is not tangent to the circle. Therefore is not smallest possible area.

>>8655733
You can have a nonequilateral triangle with all its bases still tangent to the circle lol.

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Inversed also counts?

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>>8655733

>>8655726
>basic 2d geometry is hard
kys brainlet

>>8655738
>an isosceles triange

>>8655747
This isn't a drawing of the problem, it's a drawing to show that your assumption is incorrect. Constructing an isosceles example is trivial.

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>>8655726
like this maybe?
I only skipped the calculus part and if I made any mistakes then the real problem probably isn't much harder as they should just be some small ones regarding factors and that.

>>8655736
Sure, but then it couldn't be isoceles.

>>8655714
https://www.youtube.com/watch?v=m1GIFsT5Yng

>>8655738
An isoceles of this type is clearly not the smallest possible area. Which was assumed, so no need to consider it.

>>8655749
sorry, I should have been more exact with my sarcastic greentext
>An isosceles triangle is drawn around a circle. Prove that the triangle is also an equilateral triangle assuming that the area of the triangle is the smallest area possible.

>>8656036
>suppose it's not equilateral, then one of the bases is not tangent to the circle

>image of non equilateral triangle with each base and edge tangent to the circle

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>>8655714
First tell me how you drew it.

>>8656053
Again, it's obvious that a right triangle with tangent bases is going to have an area greater than an isoceles where one of the bases isn't tangent. Since it was assumed that the triangle was smallest area, all right triangles can be ignored. My original post wasnt a complete proof, just an outline of how to go about it.

>>8655802
Shut the fuck up retard, you're wrong

>>8656226
Prove it
:^)

>>8656194
>it's obvious
not a proof, i hope you haven't convinced yourself that you actually know how to do the problem because it doesn't sound like you even understand the problem statement

>>8655714
by symmetry, the triangle is equilateral

t. physicist

>>8656257
could one actually prove it like that?

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i'm not understanding this "minimum area" statement. is it not reasonable that you can draw this? where did it say you had to make the lines tangent? is there some law that i am not understanding? is it not possible to draw this in such a way that the circle only intersects in 3 points?

>>8656286
oh nevermind, now that i see it i get it

>>8656270
why not? proofs are only as formal as the reader needs them to be

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>>8655714

>>8656440
G E O M E T R I C

>>8655714
Calculus of variations with additional boundary conditions should be able to solve this in one quick go.

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>>8656440

I suppose if you hit the perfect G it would draw itself, wouldn't it?

The G-spot?

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>>8657117

How do perpendicular overlaying realities work?

https://www.youtube.com/watch?v=AMBEprP6xps

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>>8657117