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.
I enjoyed this one so I thought I'd share it here. It's quite hard.
An isosceles triangle is drawn around a circle...
Anthony Powell
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Anthony Watson
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.
Benjamin Hughes
The hardest part here is deriving the equation.
David Watson
Easy. Suppose it's not equilateral, then one of the bases is not tangent to the circle. Therefore is not smallest possible area.
Adrian Campbell
You can have a nonequilateral triangle with all its bases still tangent to the circle lol.
Eli Johnson
Inversed also counts?
Liam Wright
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Joseph Smith
>basic 2d geometry is hard
kys brainlet
Matthew Miller
>an isosceles triange
Logan Barnes
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.
Christian Sanders
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.
Ayden Nelson
Sure, but then it couldn't be isoceles.
Ian Collins
Blake Gutierrez
An isoceles of this type is clearly not the smallest possible area. Which was assumed, so no need to consider it.
Carson Fisher
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Austin King
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.
Leo Sanchez
>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
Nicholas Garcia
First tell me how you drew it.
Robert Cooper
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.
Elijah White
Shut the fuck up retard, you're wrong
Grayson Baker
Prove it
:^)
Blake Bailey
>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
Owen Jackson
by symmetry, the triangle is equilateral
t. physicist
Julian Martinez
could one actually prove it like that?
Ian Edwards
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?
William Russell
oh nevermind, now that i see it i get it
Joseph Jenkins
why not? proofs are only as formal as the reader needs them to be
Gavin Collins
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Nicholas Cooper
G E O M E T R I C
Adrian Nguyen
Calculus of variations with additional boundary conditions should be able to solve this in one quick go.
Xavier Foster
I suppose if you hit the perfect G it would draw itself, wouldn't it?
The G-spot?
Asher Smith
How do perpendicular overlaying realities work?
Anthony Sanders
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