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Question Number 183380 by Shrinava last updated on 25/Dec/22

$$\mathrm{a}>0,\mathrm{b}>0$$ $$\{\begin{array}{l}{(\mathrm{x}-1)}^2+{(\mathrm{y}-7)}^2={\mathrm{a}}^2\\ {(\mathrm{x}-2)}^2+{(\mathrm{y}-3)}^2={\mathrm{b}}^2\end{array}$$ $$\mathrm{Find}:{(\mathrm{a}+\mathrm{b})}_{\mathbf{min}}=?$$

Commented byFrix last updated on 25/Dec/22

$$\sqrt{17}=\mathrm{the}\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{centers}$$ $$\mathrm{If}\mathrm{we}\mathrm{see}\mathrm{it}\mathrm{as}\mathrm{two}\mathrm{independent}\mathrm{circles}$$ $$\mathrm{obviously}\mathrm{the}\mathrm{limit}\mathrm{of}\mathrm{the}\mathrm{minimum}\mathrm{is}0$$

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