geometry goofy

[jagged burrow]

a quadralateral has 3 externally tangent circles of radi 1,1, and 2. What is the smallest possible area of this quadrilateral? I got 8, and its pretty obvious i just did 2*4

[solemn blaze]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[lunar shoal]

@umbral perch

[jagged burrow]

<@&775784618955505685>

pls help

[umbral perch]

what the FUCK is going on

[jagged burrow]

isnt this person breaking the rules

i just post a question

i think this person is breaking rules

[lunar shoal]

this person broke rule 1

[jagged burrow]

yeah

💀

bro what

[umbral perch]

ban

@mental elk last words?

[jagged burrow]

what kind of last words is that 💀

bro used bribery

[lunar shoal]

at least back in the day trolls were creative

[umbral perch]

ahem

[jagged burrow]

wut

[umbral perch]

thank you for pinging, i will assist your future reincarnations in cleansing this server

[jagged burrow]

whats that mean

[topaz basin]

What precisely is an "externally tangent circle"? Like, can you draw a picture of this situation?

[jagged burrow]

i cant draw a picture

but basically

it means it has 3 circles which are tangent to the outside

of the quadrilateral

like

3 circles, tangent to 3 sides

you can also google it

[topaz basin]

...a circle of any radius can be tangent to a line segment, though.

Like, the radii don't give us any information at all because they could literally be any positive real number.

[topaz basin]

Can I see the original question?

[somber parcel]

0?
the quadrilateral is in the centre lol

[topaz basin]

So the situation you're actually describing is one wherein three circles with radii 1, 1, and 2 are tangent to each other, and there exists a quadrilateral tangent to all three?

[somber parcel]

nah they can overlap

nvm I see what you mean

the three circles are tangent at one point and the quadrilateral can be placed there because that’s how you minimize area

[topaz basin]

...can these three circles be tangent at a single point?

[somber parcel]

can tangents overlap

like that

[topaz basin]

...no. Because by definition, two figures are only "tangent" if they intersect at exactly one point. The top circle intersects the other two at two points.

[somber parcel]

ah I see

[jagged burrow]

i think it just means that one side is left open

[jagged burrow]

the original question is: Find the minimal possible area of a quadrilateral which contains three externally tangent circles of radius 1,1,2

[somber parcel]

what

what do the circles have to do with anything

where is this from

[topaz basin]

...no, the original original question. A picture of the text of the question as written in wherever you got it from.

[full pier]

ah so drawing our 1-1-2 circles what is the minimal area quadrilateral we can circumscribe around it

[topaz basin]

...no.

Oh, wait.

[full pier]

do you possess some special insight about what the original question meant?

it might well be a rectangle

[topaz basin]

No, I'm just an idiot and didn't notice the important ways in which what they said now differed from what they said then.

[full pier]

hm

[topaz basin]

In the OP, they said the quadrilateral "has" the externally tangent circles, not that it "contains" them.

[full pier]

ah

[jagged burrow]

i cannt since im on computer and this is on paper

[jagged burrow]

no

the circles are outside the quadrilatera

[full pier]

oh so whats the minimal area quadrilateral inside the curved triangle area

that is tangent to each circle on at least 1 side

?

well, there is no minimum

for that

so thats not it

[topaz basin]

...no, no they aren't. Because the quadrilateral contains them.

[full pier]

agreed

[jagged burrow]

it says contains three EXTERNALLY tangent

so

this quadrilateral

synonym of contains=has

has 3 externally tangent circles

[full pier]

no

the circles are externally tangent to each other

contains means they are inside it

unless when you see an object next to a box you would describe the box as containing the object

as well, the interpretation with the quadrilateral inside has no answer technically

[jagged burrow]

no

then why is it externally tangent circles

whats the point of the word externally then

[full pier]

because they are externally tangent to each other

[jagged burrow]

ok...

oHH

THAT MAKES SENSE NOW

ok so how sould i do this

[full pier]

uh, draw a picture

[jagged burrow]

ok i did

so the height of the quadrialteral is 4

can you do it and do you get 12+8sqrt2

[full pier]

that is exactly what i got

[jagged burrow]

ok

thanks

alot

you are really smart

[full pier]

nah