2021 April MIMC 10 Problems/Problem 18
What can be a description of the set of solutions for this: ?
Two overlapping circles with each area
.
Four not overlapping circles with each area
.
There are two overlapping circles on the right of the
-axis with each area
and the intersection area of two overlapping circles on the left of the
-axis with each area
.
Four overlapping circles with each area
.
There are two overlapping circles on the right of the
-axis with each area
and the intersection area of two overlapping circles on the left of the
-axis with each area
.
Solution
First, we want to graph this equation. use the technique of absolute value, there will be four cases of . The four cases are all circles with radius of
. However, we realize that
does not have an absolute value sign, so the left side is different from the right. Therefore, our answer would be
.