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Question Number 103165 by ajfour last updated on 13/Jul/20

Commented by ajfour last updated on 13/Jul/20

$$Ifoutercirclehasunitradius,$$$$findsideoftheequilateral△.$$$$P,Q,Rarecentresofthe$$$$smallercircles.Alsofind\alpha .$$

Commented by mr W last updated on 13/Jul/20

$$radiusofsmallcircles=r$$$$\frac{2}{3}\times \sqrt{3}r+r=1$$$$\Rightarrow r=2\sqrt{3}-3$$$$\alpha =30°$$$$s=\frac{2r}{\sqrt{3}}+\frac{2\times 2r}{\sqrt{3}}=2\sqrt{3}r=6(2-\sqrt{3})$$

Commented by ajfour last updated on 13/Jul/20

$$ExcellentSir,understood,$$$$thanksalot!$$

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