Question Number 104516 by Quvonchbek last updated on 22/Jul/20
Commented by mr W last updated on 22/Jul/20
$${Red}\:{length}={r}_{\mathrm{1}} \pi+{r}_{\mathrm{2}} \pi=\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)\pi \\ $$$$={R}\pi={blue}\:{length} \\ $$$$\Rightarrow\beta=\mathrm{1} \\ $$
Answered by Rasheed.Sindhi last updated on 22/Jul/20
$${Blue}\:{length}=\pi{R} \\ $$$${Big}\:{red}\:{semicircle}=\pi{r} \\ $$$$\:{Small}\:{red}\:{semicircle}=\pi\left({R}−{r}\right) \\ $$$$\:{Red}\:{length}=\pi{r}+\pi\left({R}−{r}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\pi{R} \\ $$$$\beta=\frac{{Red}\:{length}}{{Blue}\:{length}}=\frac{\pi{R}}{\pi{R}}=\mathrm{1} \\ $$$$ \\ $$