The necessary and sufficient condition for two circles to be inscribed is that the center distance is equal to the difference of radii.

Namely:

What if? What is the distance between the centers of two circles? Equal to? What about the difference in radius? Inscribe two circles.

What if? So, carved two circles? What is the distance between the centers of two circles? Equal to? Radius difference?

Your teacher's painting is a bit rough. I'll give you a better picture.

Elliptic property: The sum of the distances from any point on the ellipse to two focal points is a constant value, which is equal to the length of the major axis.

Namely:

MF2？ +? MF 1？ =? 2a？

MF2 is the diameter of circle b, then:

r？ =? MF2？ /? 2

If the principal axis is the diameter of circle a, then:

r？ =? a

AB is the center distance and the center line of the triangle MF 1F2, then:

d？ =? AB？ =? MF 1？ /? 2

Because:

r？ +? d？ =? (MF2？ /? 2)? +? (MF 1？ /? 2)=? (MF 1？ +? MF2)/2？ =? 2a？ /? 2? =? Answer? =? r？ Namely. r？ +? d？ =? rare

Then: d? =? r？ -? r？ That is to say, the distance between the centers of two circles is equal to the difference of radii.

So the two circles are inscribed.