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Question Number 160618 by amin96 last updated on 03/Dec/21

Answered by mr W last updated on 03/Dec/21

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

$$a,b,c=radii$$$${(a+b)}^2-{(a-b)}^2={\left(2a\right)}^2-{\left(2b\right)}^2$$$$ab=a^2-b^2$$$$\Rightarrow b=\frac{(\sqrt{5}-1)a}{2}$$$${(2a-c)}^2-c^2={(a+b)}^2-{(a-b)}^2$$$$\Rightarrow c=a-b=\frac{(3-\sqrt{5})a}{2}$$$$A:B:C=a^2:b^2:c^2=1:\frac{3-\sqrt{5}}{2}:\frac{7-3\sqrt{5}}{2}$$$$\approx 1:0.382:0.146$$

Commented by Tawa11 last updated on 03/Dec/21

$$\mathrm{Great}\mathrm{sir}$$

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