Find the length of PC Here PE is the tangent of the two circle. PA = 12 ; CD/AB = 2
 Find the length of PC [Source: BDMO]
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By power of a point, $PA \cdot PD = PE^2$ and $PB \cdot PC = PE^2$. Thus, 
$$ \frac{PB}{PA} = \frac{PD}{PC}$$
and since $PB = PA + AB$ and $PD = PC + CD$, this implies
$$ 1 + \frac{AB}{PA} = 1 + \frac{CD}{PC}.$$
Subtracting 1 from both sides and solving for $PC$ yields
$$ PC = \frac{CD \cdot PA}{AB} = 2 \cdot 12 = \boxed{24}.$$
