## anonymous 5 years ago anyone have questions ask me :D

1. anonymous

I have one!

2. anonymous

and what is it?

3. myininaya

no you cannot go to the bathroom

4. anonymous

How could you position 100 circles to intersect the maximum number of times?

5. anonymous

your teacher must be a feather cuz i dont know that one

6. anonymous

lol

7. anonymous

lol

8. anonymous

no ideas on how to start it?

9. anonymous

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?

10. anonymous

Nothing that all it asks... thats why I am not sure where to begin.

11. anonymous

same radius but different centers... I think that is used to throw me off tho...

12. anonymous

well, the question is actually asking you, somehow, to determine the center!

13. anonymous

centers*

14. anonymous

I do know a circle intersects another circle twice

15. anonymous

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.

16. anonymous

Do you think this will be a formula answer?

17. anonymous

Does my last answer make sense to you?

18. anonymous

umm...they intersect maximum number of times?... no

19. anonymous

What is an intersection?!

20. anonymous

cross.. meet at a point

21. anonymous

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.

22. anonymous

ok yes... that makes sense

23. anonymous

That's only valid if they have the same radius.

24. anonymous

If they are with different radii, then they will not intersect at all when they have the same center.

25. anonymous

How are you figuring this out? Are these rules of circles?

26. anonymous

Not really, just think about it. It's very clear.

27. anonymous

ok so these are same radius different centers... how would I poistion 100 circles?

28. anonymous

oh the question says they have to have different centers?!

29. anonymous

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.

30. anonymous

It was an a., b., c. type question. so I am not sure if it even pertains

31. anonymous

I think the max will be if all of them intersect at the center of some other circle.

32. anonymous

I would roughly say that each circuit has to intersect the others at two points.

33. anonymous

each one of the other circuits at two points*

34. anonymous

Is the question asking about the number of maximum intersection points?

35. anonymous

no just how to position 100 circles to intersect the maximum number of times

36. anonymous

Ok, as I say in a position such that each circuit would intersect twice with each one of the 99 remaining circuits.

37. anonymous

I am not sure of that answers the question.

38. anonymous

ok... I understand that....

39. anonymous

What do you think polpak?

40. anonymous

One sec

41. anonymous

42. anonymous

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?

43. anonymous

100 times 2 = 200 a circles intersects twice... ???

44. anonymous

i hax a question

45. anonymous

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).

46. anonymous

that will space them evenly at any rate.

47. anonymous

i haz a question, can you answer it plzzz????

48. anonymous

while still having each circle intersecting each other circle twice.

49. anonymous

Oh wow... so would that formula be the answer or plug in the numbers

50. anonymous

Thank you