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A plane contains points A and B withAB=1LET S be the union of all disk of radius1 in the plane that cover AB Area of S=?

+2 votes
asked Aug 16, 2016 in Mathematics by Rahul Roy (7,955 points)
commented Aug 16, 2016 by vikash (21,287 points)
please check the question.

1 Answer

+2 votes
answered Aug 16, 2016 by vikash (21,287 points)
selected Aug 18, 2016 by Rahul Roy
Best answer

Solution to the above question:

As the red circles move about segment $AB$, they cover the area we are looking for. On the left side, the circle must move around pivoted on $B$. On the right side, the circle must move pivoted on $A$ However, at the top and bottom, the circle must lie on both A and B, giving us our upper and lower bounds.

This egg-like shape is $S$.

The area of the region can be found by dividing it into several sectors, namely

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