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Question Number 152740 by mr W last updated on 31/Aug/21

Commented by mr W last updated on 31/Aug/21

$$\left[Q152712\right]$$

Answered by mr W last updated on 31/Aug/21

Commented by mr W last updated on 31/Aug/21

$$AF=CL$$$$EO=\frac{CL}{2}$$$$LM=\frac{2}{3}\times EO=\frac{CL}{3}$$$$CM=\frac{2}{3}\times CL$$$$\Rightarrow \frac{CL}{CM}=\frac{3}{2}$$$$GF=\frac{CN}{2}$$$$MN=\frac{AG}{3}\Rightarrow AG=3\times MN$$$$AG+GF=AF=CL$$$$3\times MN+\frac{CN}{2}=CL...\left(i\right)$$$$MN+CN=\frac{2}{3}\times CL...\left(ii\right)$$$$3\times \left(ii\right)-\left(i\right):$$$$\frac{5}{2}\times CN=CL$$$$\Rightarrow \frac{CL}{CN}=\frac{5}{2}$$$$\frac{CL}{CL}+\frac{CL}{CM}=1+\frac{3}{2}=\frac{5}{2}=\frac{CL}{CN}$$$$\Rightarrow \frac{1}{CL}+\frac{1}{CM}=\frac{1}{CN}$$

Commented by Tawa11 last updated on 31/Aug/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}\mathrm{sir}.$$

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