anonymous
  • anonymous
"A plane contains points A and B with AB=1. Let S be the union of all disks of radius 1 in the plane that cover AB. What is the area of S?" As taken from the 2004 AMC. Here's a math challenge for those of you who like math. ;)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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bahrom7893
  • bahrom7893
oh dang... there are just way too many circles to graph till u get to the outermost (union of all of them)
bahrom7893
  • bahrom7893
and then u gotta subtract some complements of the intersection, uhmm no thanks!
anonymous
  • anonymous
lol

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anonymous
  • anonymous
Too many circles to graph? Nonsense. You have two points connected by a line, the circles just pivot on each one.
anonymous
  • anonymous
And then you have the circles that must lie on both A and B.
anonymous
  • anonymous
I'm not redrawing it here, but you have two sectors with area 4pi/3, two sectors with area pi/6, and the intersection has area sqrt(3)/2. Answer should be 8pi/3+pi/3-sqrt(3)/2=3pi-sqrt(3)/2
bahrom7893
  • bahrom7893
But he's asking for a union of everything
bahrom7893
  • bahrom7893
i see six minimum
anonymous
  • anonymous
Right you are, Sir! Here, have several solutions.
anonymous
  • anonymous
S is the union of all the disks, but it asks for the area of S, not the area of all the disks.

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