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Question Number 94508 by john santu last updated on 19/May/20

Answered by mr W last updated on 19/May/20

$$OD=DB=\frac{6}{\sqrt{2}}=3\sqrt{2}$$$$OE=ED=OA=6$$$$\cos \mathrm{\angle }ODE=\frac{OD}{2ED}=\frac{\sqrt{2}}{4}$$$${OC}^2={OD}^2+x^2+2ODx\times \frac{\sqrt{2}}{4}$$$$36=18+x^2+3x$$$$(x-3)(x+6)=0$$$$\Rightarrow x=3$$$$$$$$or$$$$EC=2\times OE\times \cos \mathrm{\angle }OED$$$$=2\times 6\times \cos (\pi -2\mathrm{\angle }ODE)$$$$=12\times (1-2\times {\left(\frac{\sqrt{2}}{4}\right)}^2)=9$$$$x=9-6=3$$

Commented by PRITHWISH SEN 2 last updated on 19/May/20

$$\mathrm{sir}\mathrm{I}\mathrm{think}\mathrm{it}\mathrm{will}\mathrm{be}$$$$\mathrm{OD}=\mathrm{DB}\left(1^{\mathrm{st}}\mathrm{line}\right)$$

Commented by mr W last updated on 19/May/20

$$yes,thanks!$$

Commented by john santu last updated on 19/May/20

great ��������

Answered by john santu last updated on 22/May/20

Commented by john santu last updated on 22/May/20

$$\Rightarrow (6-\mathrm{y})(6+\mathrm{y})=6x$$$$\Rightarrow 36-{\mathrm{y}}^2=6x\left(i\right)$$$$\Rightarrow {2\mathrm{y}}^2=36;{\mathrm{y}}^2=18\left(\mathrm{ii}\right)$$$$\mathrm{then}\mathrm{we}\mathrm{get}36-18=6x$$$$6x=18;x=3$$

Commented by i jagooll last updated on 22/May/20

$$\mathrm{waw}.....$$

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