Question

$AB$ and $CD$ are two common tangents to circles which touch each other at $C$. If $D$ lies on $AB$ such that $CD=4cm$, then what is the length of $AB$.

Answer 1

$\begin{array}{c}Firstcircle\\ \Rightarrow AD=DC\\ \Rightarrow DC=4cm\\ \Rightarrow AD=4cm\\ fro\sec ondcircle\\ \Rightarrow DC=DB=4cm\\ \Rightarrow AB=AD+DB\\ \therefore AB=8cm\end{array}$