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To arrange 3 algebra books and 3 geometry books on a shelf so that no two books of the same type are next to each other, you can use the concept of permutations. There are 3! ways to arrange the algebra books and 3! ways to arrange the geometry books. This gives a total of 3! * 3! = 36 ways to arrange the books on the shelf such that no two books of the same type are next to each other.
No never!
Parallel lines never touch each other and remain equal distance from each other
two lines that do not touch each other
No; tangent circles touch each other at one point but concentric circles cannot not touch.