How many Positions do two circles have? Let's try to explore it using GSP!

Here is GSP file.

A. In the case of the given two circles having same length of radius.

1.No Intersections 2. Circumscription

3.Intersect 4.Consistence

B. In the case of the given two circles having the different length of radiuses.

5. No Intersections 6. Circumscription

7.Intersect 8.Inscription 9. Inclusion

In the case of the given two circles with the one circle is external to the tangent circle and the another internal. Here is GSP file.

A. The given two circles having same length of radius.		B. The given two circles having the different length of radiuses.
1. No intersection		5. No intersection
2. Circumscription		6. Circumscription
3. Intersect		7. Intersect
4. Consistence		8. Inscription
		9. Inclusion

In the case of the given two circle are both external or internal to the tangent circle. Here is GSP file.

A. The given two circles having same length of radius.		B. The given two circles having the different length of radiuses.
1. No intersection		5. No intersection
2. Circumscription		6. Circumscription
3. Intersect		7. Intersect
4. Consistence		8. Inscription
		9. Inclusion

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