Combining Functions Into One Equation

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I was wondering if anyone could help with this problem I've been having.

I want to do something similar to the famous Batman equation where multiple smaller functions used to make small parts of the Batman logo were combined into one giant equation.

The way this was achieved was by setting all of the smaller functions equal to zero, multiplying them all together, and setting the final equation equal to zero.

This is the shape I'm trying to achieve

As you can see I have the individual lines figured out, the first one obviously being the circle and the other two the lines. When I multiply them together the huge radical that restricts the range of the lines distributes to the circle and deletes it but I was wondering if there was any way to stop that. Is there any way to combine the three equations into one?