"Coplanar" means "on the same plane". For example, if a laser gun shot straight through the center of both circles, then unless they both have the same center, it wouldn't just pierce the two circles, but would slice them clean in half.
In simple terms, the definition of "plane" is "a flat surface". In mathematics, this means a 2-dimensional surface that extends in every compass direction (or at least if the compass were held in a certain position). This is also known as an "affine space of rank 2".
In three dimensions, any plane can be described by ax+by+cz=d. Using that along with the equations for both circles, you should be able to solve for a,b,c,d. If you can't, they aren't coplanar.
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Tangential circles.
Concentric Circle
They're definitely similar, concentric, and coplanar. They're not necessarily congruent, but they could be.
Coplanar means "on the same plane", so we can imagine that non coplanar means "not on the same plane".For example, if you draw a square and point on a piece of paper, the two objects are coplanar. However, if we were to add depth and the objects were a distance apart, they are said to be non coplanar.
3 coplanar points may or may not be collinear. 3 collinear points must be coplanar.