CircleHardBloom L3
Question
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 $C_{2}$.
Solution
Sol. [Key Concept: Two circles with no common point: classify by centre-distance vs $r_{1} + r_{2}$ and ${|r}_{1} - r_{2}|$.]
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