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Question Number 155701 by ajfour last updated on 03/Oct/21

Commented by ajfour last updated on 03/Oct/21

$$Ifthebluetriangleisequilateral$$$$findtheradiusratio.$$$$(thecenterofbothcircleslieonthe$$$$samevertical)$$

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

$$bothcircleshavethesamecenter.$$$$radiusofsmallcircler$$$$radiusofbigcircleR$$$$R=\sqrt{r^2+{\left(\frac{2r}{\sqrt{3}}\right)}^2}=r\sqrt{\frac{7}{3}}$$$$\Rightarrow \frac{r}{R}=\sqrt{\frac{3}{7}}=\frac{\sqrt{21}}{7}\approx 0.654$$

Commented by ajfour last updated on 04/Oct/21

$$Thankyousir.$$$$sir,whatifsbesideof{△}_{eq},$$$$with\left(\frac{s}{r}\right)={\left(\frac{s}{r}\right)}_{max};\frac{R}{r}=?$$

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