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
$$\boldsymbol{\mathrm{Is}}\:\boldsymbol{\mathrm{it}}\:\mathrm{43}.\mathrm{86}\:? \\ $$
Commented by TawaTawa last updated on 30/Sep/19
$$\mathrm{Find}\:\mathrm{distance}\:\:\mathrm{EF} \\ $$
Commented by TawaTawa last updated on 30/Sep/19
$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{sir} \\ $$
Commented by Prithwish sen last updated on 30/Sep/19
$$\mathrm{OC}=\sqrt{\mathrm{20}^{\mathrm{2}} +\mathrm{15}^{\mathrm{2}} }\:=\:\mathrm{25}\:\mathrm{the}\:\mathrm{radius} \\ $$$$\mathrm{OG}=\:\mathrm{12}.\mathrm{5}\:\mathrm{Let}\:\mathrm{OD}=\mathrm{l}\:\:\mathrm{DB}=\mathrm{b}\:\mathrm{and}\:\mathrm{DG}=\mathrm{a} \\ $$$$\boldsymbol{\mathrm{l}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\boldsymbol{\mathrm{OG}}^{\mathrm{2}} =\mathrm{12}.\mathrm{5}^{\mathrm{2}} ….\left(\mathrm{i}\right) \\ $$$$\boldsymbol{\mathrm{l}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} =\boldsymbol{\mathrm{OB}}^{\mathrm{2}} =\mathrm{15}^{\mathrm{2}} …….\left(\mathrm{ii}\right) \\ $$$$\mathrm{from}\:\left(\mathrm{i}\right)\:\mathrm{and}\:\left(\mathrm{ii}\right)\:\mathrm{we}\:\mathrm{get}\:\mathrm{b}=\mathrm{9}\:\left(\mathrm{as}\:\mathrm{a}+\mathrm{b}=\mathrm{12}.\mathrm{5}\right) \\ $$$$\therefore\mathrm{l}=\mathrm{12} \\ $$$$\therefore\:\boldsymbol{\mathrm{DF}}^{\mathrm{2}} +\boldsymbol{\mathrm{l}}^{\mathrm{2}} =\boldsymbol{\mathrm{OF}}^{\mathrm{2}} \Rightarrow\boldsymbol{\mathrm{DF}}=\sqrt{\mathrm{481}} \\ $$$$\therefore\:\boldsymbol{\mathrm{EF}}\:=\:\mathrm{2}\boldsymbol{\mathrm{DF}}=\mathrm{2}\sqrt{\mathrm{481}}\:=\:\mathrm{43}.\mathrm{86}\: \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{check}}. \\ $$
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
$$\mathrm{You}\:\mathrm{consider}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{tbe}\:\bigtriangleup\mathrm{OAB}. \\ $$$$\mathrm{Great}\:\mathrm{sir}. \\ $$
Commented by mr W last updated on 30/Sep/19
$${OF}={OC}={AB}=\sqrt{\mathrm{15}^{\mathrm{2}} +\mathrm{20}^{\mathrm{2}} }=\mathrm{25} \\ $$$${OG}×{AB}=\mathrm{15}×\mathrm{20} \\ $$$$\Rightarrow{OG}=\frac{\mathrm{15}×\mathrm{20}}{\mathrm{25}}=\mathrm{12} \\ $$$${FG}=\sqrt{\mathrm{25}^{\mathrm{2}} −\mathrm{12}^{\mathrm{2}} }=\sqrt{\mathrm{481}} \\ $$$${EF}=\mathrm{2}\sqrt{\mathrm{481}} \\ $$
Commented by TawaTawa last updated on 30/Sep/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$