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Question Number 70048 by TawaTawa last updated on 30/Sep/19

Commented by TawaTawa last updated on 30/Sep/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by Prithwish sen last updated on 30/Sep/19

$$\mathbf{Is}\mathbf{it}43.86?$$

Commented by TawaTawa last updated on 30/Sep/19

$$\mathrm{Find}\mathrm{distance}\mathrm{EF}$$

Commented by TawaTawa last updated on 30/Sep/19

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{the}\mathrm{answer}\mathrm{sir}$$

Commented by Prithwish sen last updated on 30/Sep/19

$$\mathrm{OC}=\sqrt{{20}^2+{15}^2}=25\mathrm{the}\mathrm{radius}$$$$\mathrm{OG}=12.5\mathrm{Let}\mathrm{OD}=\mathrm{l}\mathrm{DB}=\mathrm{b}\mathrm{and}\mathrm{DG}=\mathrm{a}$$$${\mathbf{l}}^2+{\mathbf{a}}^2={\mathbf{OG}}^2=12.5^2....\left(\mathrm{i}\right)$$$${\mathbf{l}}^2+{\mathbf{b}}^2={\mathbf{OB}}^2={15}^2.......\left(\mathrm{ii}\right)$$$$\mathrm{from}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right)\mathrm{we}\mathrm{get}\mathrm{b}=9(\mathrm{as}\mathrm{a}+\mathrm{b}=12.5)$$$$\therefore \mathrm{l}=12$$$$\therefore {\mathbf{DF}}^2+{\mathbf{l}}^2={\mathbf{OF}}^2\Rightarrow \mathbf{DF}=\sqrt{481}$$$$\therefore \mathbf{EF}=2\mathbf{DF}=2\sqrt{481}=43.86$$$$\mathbf{please}\mathbf{check}.$$

Commented by Prithwish sen last updated on 30/Sep/19

Answered by mr W last updated on 30/Sep/19

Commented by Prithwish sen last updated on 01/Oct/19

$$\mathrm{You}\mathrm{consider}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{tbe}△\mathrm{OAB}.$$$$\mathrm{Great}\mathrm{sir}.$$

Commented by mr W last updated on 30/Sep/19

$$OF=OC=AB=\sqrt{{15}^2+{20}^2}=25$$$$OG\times AB=15\times 20$$$$\Rightarrow OG=\frac{15\times 20}{25}=12$$$$FG=\sqrt{{25}^2-{12}^2}=\sqrt{481}$$$$EF=2\sqrt{481}$$

Commented by TawaTawa last updated on 30/Sep/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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