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Question Number 37691 by MJS last updated on 16/Jun/18

$$\mathrm{Sir}\mathrm{Aifour},\mathrm{I}\mathrm{just}\mathrm{answered}\mathrm{your}\mathrm{question}$$$$\mathrm{number}37209...\mathrm{greetings}\mathrm{from}\mathrm{a}\mathrm{rainy}$$$$\mathrm{Saturday}\mathrm{evening}\mathrm{in}\mathrm{Vienna},\mathrm{Austria}!$$

Commented by ajfour last updated on 16/Jun/18

$$rainyevenuphere,Sir$$$$i^{\prime }lltryandfollowyoursolution.$$

Commented by MJS last updated on 16/Jun/18

$$\mathrm{the}\mathrm{idea}\mathrm{is}\mathrm{simple},\mathrm{but}\mathrm{the}\mathrm{equations}\mathrm{get}$$$$\mathrm{harder}\mathrm{to}\mathrm{simplify}\mathrm{from}\mathrm{step}\mathrm{to}\mathrm{step}$$$$\mathrm{the}\mathrm{method}\mathrm{is}\mathrm{easy}\mathrm{to}\mathrm{explain}:$$$$\mathrm{just}\mathrm{think}\mathrm{about}\mathrm{the}\mathrm{required}\mathrm{distances}$$$$\mathrm{between}\mathrm{the}\mathrm{centers}$$$$2\mathrm{circles}\mathrm{touching}\mathrm{from}\mathrm{outside}:$$$${\mathrm{distance}}^2={\left(\mathrm{sum}\mathrm{of}\mathrm{radii}\right)}^2$$$$2\mathrm{circles}\mathrm{touching},\mathrm{one}\mathrm{inside}\mathrm{the}\mathrm{other}:$$$${\mathrm{distance}}^2={\left(\mathrm{difference}\mathrm{of}\mathrm{radii}\right)}^2$$

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