If a variable circle K touches a fixed circle K1 and is orthogonal to another fixed circle K2, using inversion, how can we show that K touches another fixed circle coaxial with K1 and K2?
If a variable circle K touches a fixed circle K1 and is orthogonal to another fixed circle K2, using inversion, how can we show that K touches another fixed circle coaxial with K1 and K2?
Invert with respect to K2. Then the variable circle is self-inverse, so it must also touch the inverse of K1.