Question-214603

Question Number 214603 by ajfour last updated on 13/Dec/24

Answered by TonyCWX08 last updated on 13/Dec/24

W h e r e i s R ?

W h e r e i s r ?

Commented by ajfour last updated on 13/Dec/24

s o r r y w r o n g q u e s t i o n

Answered by mr W last updated on 13/Dec/24

Commented by mr W last updated on 13/Dec/24

{(R - r)}^{2} = R^{2} + {(2 r)}^{2} - 4 R r \cos 30 °

2 (\sqrt{3} - 1) R = 3 r

\Rightarrow \frac{R}{r} = \frac{3}{2 (\sqrt{3} - 1)} = \frac{3 (\sqrt{3} + 1)}{4} \approx 2.049

Answered by A5T last updated on 13/Dec/24

\sqrt{{(R - r)}^{2} - r^{2}} = R - \sqrt{{(2 r)}^{2} - r^{2}}

\Rightarrow \sqrt{R (R - 2 r)} = R - r \sqrt{3}

\Rightarrow R^{2} - 2 r R = R^{2} + 3 r^{2} - 2 R r \sqrt{3}

\Rightarrow 2 R r (\sqrt{3} - 1) = 3 r^{2} \Rightarrow \frac{R}{r} = \frac{3}{2 (\sqrt{3} - 1)} = \frac{3 (\sqrt{3} + 1)}{4}

Commented by ajfour last updated on 13/Dec/24

T h a n k y o u! P r o m p t w a y s!

Commented by ajfour last updated on 13/Dec/24

https://youtu.be/z1RwkyYqV34?si=luatRZ1-3shsgmnX