Let the circle $C_{1}:|z| = r$ and $C_{2}:|z - 3 - 4i| = 5,z \in \mathbb{C}$, be such that $C_{2}$ l

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Let the circle $C_{1}:|z| = r$ and $C_{2}:|z - 3 - 4i| = 5,z \in \mathbb{C}$, be such that $C_{2}$ lies within $C_{1}$. If $z_{1}$ moves on $C_{1},z_{2}$ moves on $C_{2}$ and $\min\left| z_{1} - z_{2} \right| = 2$, then max $\left| z_{1} - z_{2} \right|$ is equal to :-

Accepted Answer

Sol. [Key Concept: Farthest points of the two circles: max distance $=$ (centre-to-centre) $+ r_{1} + r_{2}$.]$${|z| = r }{OA = r }$$minimum $\left| z_{1} - z_{2} \right| = 2$$$\Rightarrow r - 10 = 2 \Rightarrow r = 12 $$maximum value of CB$$\left| z_{1} - z_{2} \right| = r + 10 = 12 + 10 = 22 $$

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