Question-159355

Question Number 159355 by mnjuly1970 last updated on 16/Nov/21

Answered by mr W last updated on 16/Nov/21

radius of small circle r=(b/2) (b/2)×(b/2)=(a−(b/2))(a+(b/2)) (b^2 /4)=a^2 −(b^2 /4) (b^2 /2)=a^2 ⇒(b/a)=(√2)

$${radius}\:{of}\:{small}\:{circle}\:{r}=\frac{{b}}{\mathrm{2}} \\ $$$$\frac{{b}}{\mathrm{2}}×\frac{{b}}{\mathrm{2}}=\left({a}−\frac{{b}}{\mathrm{2}}\right)\left({a}+\frac{{b}}{\mathrm{2}}\right) \\ $$$$\frac{{b}^{\mathrm{2}} }{\mathrm{4}}={a}^{\mathrm{2}} −\frac{{b}^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\frac{{b}^{\mathrm{2}} }{\mathrm{2}}={a}^{\mathrm{2}} \\ $$$$\Rightarrow\frac{{b}}{{a}}=\sqrt{\mathrm{2}} \\ $$

Commented by mr W last updated on 16/Nov/21