Question

$C_1$ and $C_2$ are two circles in a plane. If $N$ is the total number of common tangents, then which of the following is wrong?

• A. $N=2$ when $C_1$ and $C_2$ intersect but do not touch
• B. $N=4$ when $C_1$ and $C_2$ are disjoint
• C. When $C_1$ and $C_2$ touch then $N$ must be $3$
• D. $N$ can never be more than $4$

Answer 1

The correct option is A $N=2$ when $C_1$ and $C_2$ intersect but do not touch

From the all images given above,

In the first image both the circles intersect and touches each other and number of tangents is 2.

Hence, option A is wrong.