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Omni-MATH / Suppose A,B,C, and D are four circles of radius r>0 centered about the points (0,r),(r,0), (0,−r), and (−r,0) in the plane. Let O be a circle centered at (0,0) with radius 2r. In t…

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problem

Suppose A,B,CA, B, C, and DD are four circles of radius r>0r>0 centered about the points (0,r),(r,0)(0, r),(r, 0), (0,−r)(0,-r), and (−r,0)(-r, 0) in the plane. Let OO be a circle centered at (0,0)(0,0) with radius 2r2 r. In terms of rr, what is the area of the union of circles A,B,CA, B, C, and DD subtracted by the area of circle OO that is not contained in the union of A,B,CA, B, C, and DD?
Plain-text mathematical notation (without MathML)
Suppose A,B,C, and D are four circles of radius r>0 centered about the points (0,r),(r,0), (0,−r), and (−r,0) in the plane. Let O be a circle centered at (0,0) with radius 2r. In terms of r, what is the area of the union of circles A,B,C, and D subtracted by the area of circle O that is not contained in the union of A,B,C, and D?
Original LaTeX notation
Suppose $A, B, C$, and $D$ are four circles of radius $r>0$ centered about the points $(0, r),(r, 0)$, $(0,-r)$, and $(-r, 0)$ in the plane. Let $O$ be a circle centered at $(0,0)$ with radius $2 r$. In terms of $r$, what is the area of the union of circles $A, B, C$, and $D$ subtracted by the area of circle $O$ that is not contained in the union of $A, B, C$, and $D$?

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Source and history

task_id
8742f96c-6f7e-5d51-b40f-f71557b33477
task_key
test--8742f96c-6f7e-5d51-b40f-f71557b33477
task_revision_id
1
config / split
/ test

Official source

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