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I have one!
and what is it?
no you cannot go to the bathroom
How could you position 100 circles to intersect the maximum number of times?
your teacher must be a feather cuz i dont know that one
no ideas on how to start it?
I think it's a good question dinabina. Does the question say anything about radius of the circles; are they all of the same size?
Nothing that all it asks... thats why I am not sure where to begin.
same radius but different centers... I think that is used to throw me off tho...
well, the question is actually asking you, somehow, to determine the center!
I do know a circle intersects another circle twice
If all circles have the same radius, then they intersect maximum number of times, when you put each one in the top of the others.
Do you think this will be a formula answer?
Does my last answer make sense to you?
umm...they intersect maximum number of times?... no
What is an intersection?!
cross.. meet at a point
if you have circle 1 with the same radius as circle 2. And you draw circle with the same center as circle 2. Then they will have infinitely many intersection points; they actually intersect for all points in the two circles.
ok yes... that makes sense
That's only valid if they have the same radius.
If they are with different radii, then they will not intersect at all when they have the same center.
How are you figuring this out? Are these rules of circles?
Not really, just think about it. It's very clear.
ok so these are same radius different centers... how would I poistion 100 circles?
oh the question says they have to have different centers?!
Is this going to be a picture answer or a formula answer?..... yeah same radius different centers.... but the question just says how would you position 100 circles to intersect the maximum number of times.
It was an a., b., c. type question. so I am not sure if it even pertains
I think the max will be if all of them intersect at the center of some other circle.
I would roughly say that each circuit has to intersect the others at two points.
each one of the other circuits at two points*
Is the question asking about the number of maximum intersection points?
no just how to position 100 circles to intersect the maximum number of times
Ok, as I say in a position such that each circuit would intersect twice with each one of the 99 remaining circuits.
I am not sure of that answers the question.
ok... I understand that....
What do you think polpak?
Take your time!
number of total points of intersection of n congruent circles = 2C(n, 2) 100 circles intersect in 2C(100, 2) = 400 points Does this look wack?
100 times 2 = 200 a circles intersects twice... ???
i hax a question
Ok, so I think for positioning them you just have to arrange their centers around some point at intervals of \(2\pi/100\) radians a distance less than r from that point (where r is the radius of each circle).
that will space them evenly at any rate.
i haz a question, can you answer it plzzz????
while still having each circle intersecting each other circle twice.
Oh wow... so would that formula be the answer or plug in the numbers