Answer : Option E

The distance between their centers could be 8 (r1+r2) or 2(r1-r2) even after combining the two statements


Since they are tangent therefore there is only one point of intersection the distance between their centers will be r1+r2 or r1-r2 (Internally tangent

But in case two points of intersection the distance between their center will be less than r1+r2 and greater than r1-r2

Also in case NO point of intersection the distance between their center will be greater than r1+r2 or lesser than r1-r2

Thank you! There must have been an error in the answer choices in my book.

The answer is NOT C, unfortunately. Two circles can be tangent externally or internally, as shown below.



If the circles are EXTERNALLY tangent, the distance is r1 + r2, or 8. If the circles are INTERNALLY tangent, the distance is |r1 - r2|, or 2. So the real answer is E.

Beware these seemingly easy questions on the test! If the answer were really C, they wouldn't bother asking you.