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anonymous
 4 years ago
"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. ;)
anonymous
 4 years ago
"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. ;)

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bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.0oh dang... there are just way too many circles to graph till u get to the outermost (union of all of them)

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.0and then u gotta subtract some complements of the intersection, uhmm no thanks!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Too many circles to graph? Nonsense. You have two points connected by a line, the circles just pivot on each one.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0And then you have the circles that must lie on both A and B.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'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/3sqrt(3)/2=3pisqrt(3)/2

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.0But he's asking for a union of everything

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Right you are, Sir! Here, have several solutions.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0S 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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