Question-127749

Question Number 127749 by ajfour last updated on 01/Jan/21

Commented by ajfour last updated on 01/Jan/21

F i n d r a t i o o f r a d i u s o f s m a l l

s e m i c i r c l e s o f e q u a l r a d i i t o

t h a t o f o u t e r s e m i c i r c l e r / R .

Answered by mr W last updated on 01/Jan/21

l e t λ = \frac{r}{R}

\frac{R - r}{R} = \frac{r}{2 R - r}

1 - λ = \frac{λ}{2 - λ}

λ^{2} - 4 λ + 2 = 0

\Rightarrow λ = 2 - \sqrt{2}

Commented by mr W last updated on 01/Jan/21

Commented by ajfour last updated on 01/Jan/21

E x c e l l e n t n o t i c e, S i r; w h a t t o s a y \dots

A H a p p Y N e w Y e a r!

Commented by mr W last updated on 01/Jan/21

t h a n k s a l o t!

h a p p y n e w y e a r t o y o u t o o!

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