Suppose that two circles `C_(1)` and `C_(2)` in a plane have no points in common. Then

Options

A. there is no line tangent to both `C_(1)` and `C_(2)`
B. there are exactly four lines tangent to both `C_(1)` and `C_(2)`
C. there are no lines tangent to both `C_(1)` and `C_(2)` or there are exactly two lines tangent to both `C_(1)` and `C_(2)`
D. there are no lines tangent to both `C_(1)` and `C_(2)` or there are exactly four lines tangent to both `C_(1)` and `C_(2)`

Answer

D

Explanation

Since `C_(1)` and `C_(2)` in a plane have no points in common, either one circle is completely lying inside other without touching it or two circles are external without intersection or touching as shown in the following figure.