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Question Number 137437 by I want to learn more last updated on 02/Apr/21

Answered by mr W last updated on 02/Apr/21

$$\frac{r-2}{r+2}=\frac{6-r}{6+r}$$$$r^2=12$$$$r=2\sqrt{3}$$

Commented by I want to learn more last updated on 02/Apr/21

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{Please}\mathrm{what}\mathrm{rule}\mathrm{did}\mathrm{you}\mathrm{use}.$$

Commented by I want to learn more last updated on 02/Apr/21

$$\mathrm{I}\mathrm{mean}\mathrm{how}\mathrm{you}\mathrm{place}\mathrm{the}\mathrm{ratio}\mathrm{sir}.$$

Commented by nadovic last updated on 03/Apr/21

$$\mathrm{The}\mathrm{circles}\mathrm{are}\mathrm{externally}\mathrm{tangential}$$$$\mathrm{and}\mathrm{also}\mathrm{have}\mathrm{common}\mathrm{intersecting}$$$$\mathrm{tangents},\mathrm{so}\mathrm{they}\mathrm{are}\mathrm{similar}.\therefore \mathrm{the}$$$$\mathrm{ratios}\mathrm{of}consecutive\mathrm{radii}\mathrm{are}\mathrm{equal}.$$$$\frac{r}{2}=\frac{6}{r}$$$$r^2=12$$$$r=2\sqrt{3}$$

Commented by mr W last updated on 03/Apr/21

Commented by I want to learn more last updated on 03/Apr/21

$$\mathrm{Thanks}\mathrm{sir},\mathrm{i}\mathrm{understand}\mathrm{it}\mathrm{better}\mathrm{now}.$$

Commented by I want to learn more last updated on 03/Apr/21

$$\mathrm{Thanks}\mathrm{sir},\mathrm{i}\mathrm{appreciate}.$$

Answered by mnjuly1970 last updated on 03/Apr/21

$$2\sqrt{2r}+2\sqrt{6r}=\sqrt{{(8+2r)}^2-16}$$$$2\sqrt{2r}+2\sqrt{6r}=\sqrt{4r^2+32r+48}$$$$2r+6r+2\sqrt{12}r=r^2+8r+12$$$$-2\sqrt{12}r+r^2+12=0$$$$r=\sqrt{12}=2\sqrt{3}$$$$$$

Commented by I want to learn more last updated on 03/Apr/21

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$

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