Question-218812

Question Number 218812 by Spillover last updated on 15/Apr/25

Answered by A5T last updated on 16/Apr/25

(√((R−x)^2 −x^2 ))=(√(x^2 −(x−h)^2 )) ⇒(R−2x)R=h(2x−h) ⇒R^2 +h^2 =2x(h+R) ⇒x=((h^2 +R^2 )/(2(h+R)))

$$\sqrt{\left(\mathrm{R}−\mathrm{x}\right)^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }=\sqrt{\mathrm{x}^{\mathrm{2}} −\left(\mathrm{x}−\mathrm{h}\right)^{\mathrm{2}} } \\ $$$$\Rightarrow\left(\mathrm{R}−\mathrm{2x}\right)\mathrm{R}=\mathrm{h}\left(\mathrm{2x}−\mathrm{h}\right) \\ $$$$\Rightarrow\mathrm{R}^{\mathrm{2}} +\mathrm{h}^{\mathrm{2}} =\mathrm{2x}\left(\mathrm{h}+\mathrm{R}\right) \\ $$$$\Rightarrow\mathrm{x}=\frac{\mathrm{h}^{\mathrm{2}} +\mathrm{R}^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{h}+\mathrm{R}\right)} \\ $$

Commented by Spillover last updated on 16/Apr/25