Question-175717

Question Number 175717 by ajfour last updated on 05/Sep/22

Answered by mr W last updated on 05/Sep/22

{(R - r)}^{2} = r^{2} + {(\frac{R}{2} + r)}^{2}

r^{2} + 3 R r - \frac{3 R^{2}}{4} = 0

\Rightarrow \frac{r}{R} = \sqrt{3} - \frac{3}{2} \approx 0.232

Commented by mr W last updated on 05/Sep/22

Commented by ajfour last updated on 05/Sep/22

E x c e l l e n t n o t i c e s i r!

Commented by ajfour last updated on 05/Sep/22

\frac{R}{r} = \frac{2}{2 \sqrt{3} - 3} = \frac{2 (2 \sqrt{3} + 3)}{3} = \frac{4}{\sqrt{3}} + 2

= \frac{4 \times 1.732}{3} + 2 = \frac{6.928}{3} + 2 \approx 4.31

Commented by Tawa11 last updated on 05/Sep/22

Great sir

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