 # MA005 Calculus 1.2.1 # 19

#1

I’m confused about the answers given for C, D, and E on # 19. The problem asks for the shortest distance between two circles and the answers given are 0, 2, and 1 respectively. The answer for C is 0 because the circles intersect. Being that the radii for D and E are 3 and 15 (for D) and 12 and 1 (for E), shouldn’t the distance between those also be 0 since they overlap? If the radius of one circle exceeds the entire distance between the two center-points, then surely the circles intersect or overlap one another. I don’t understand why C is 0 but not D and E.

#2

For both (d) and (e), the circles overlap. I’m a long way out from geometry, but note in the answer key that the arithmetic for (d) and (e) changes to [long radius] - [distance between centers] - [short radius].

A visual check confirms the answers for the shortest distance between points on the circles; for example here is (e) graphed (by the way, Desmos is pretty fun to play with!):

https://www.desmos.com/calculator/fj8d2a8vvz

#3

So it’s asking for the distance between the outer edges of the circles even if one circle is inside the other? Okay, that makes sense now. The circle the question is referring to is only the line of the perimeter and not the entire area of the circle inside.