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**Geometry Problem Involving Circles and Fixed Radius- Please Help!**

**I have a compass with radius X, and my friend has a compass with radius Y. We both draw a circle with our compasses so that our circles intersect at two points. Call these two points C and D.**

You draw a common tangent to both circles, meeting my circle at point A and my friends circle at point B. Prove that the circles passing through A, B and C are the same, regardless of where my friend and I draw our circles, and they are the same as the radius of the circle going through A, B and D.

You draw a common tangent to both circles, meeting my circle at point A and my friends circle at point B. Prove that the circles passing through A, B and C are the same, regardless of where my friend and I draw our circles, and they are the same as the radius of the circle going through A, B and D.

**I can solve this problem for X=Y, but i dont know how to do any other cases**