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Question Number 153915 by liberty last updated on 12/Sep/21

Answered by mr W last updated on 12/Sep/21

Commented by mr W last updated on 12/Sep/21

$$AQ=\frac{11}{2}-4=\frac{3}{2}$$$$DQ={\left(\frac{\frac{3}{2}}{4}\right)}^2\times 12=\frac{27}{16}$$$$AC=12-DQ=12-\frac{27}{16}=\frac{165}{16}$$$$\frac{BC}{AB}=\frac{OC}{AQ}=\frac{4}{\frac{3}{2}}=\frac{8}{3}$$$$\frac{\frac{165}{16}-AB}{AB}=\frac{8}{3}$$$$\frac{\frac{165}{16}}{AB}=\frac{11}{3}$$$$AB=\frac{165}{16}\times \frac{3}{11}=\frac{45}{16}$$$$ER=DQ+AB=\frac{27}{16}+\frac{45}{16}=\frac{9}{2}$$$$ER={\left(\frac{BR}{4}\right)}^2\times 12=\frac{9}{2}$$$$\Rightarrow BR=\sqrt{6}$$$$shadedarea=\frac{2}{3}\times BR\times ER$$$$=\frac{2}{3}\times \sqrt{6}\times \frac{9}{2}=3\sqrt{6}$$

Commented by Tawa11 last updated on 12/Sep/21

$$\mathrm{Weldone}\mathrm{sir}.$$

Commented by mr W last updated on 12/Sep/21

$$canyourcommentbeunderstoodthat$$$$theansweriscorrect?$$

Commented by Tawa11 last updated on 12/Sep/21

$$\mathrm{No}\mathrm{sir},\mathrm{I}\mathrm{am}\mathrm{going}\mathrm{through}\mathrm{your}\mathrm{workings}.\mathrm{Learning}\mathrm{the}\mathrm{steps}.$$

Commented by liberty last updated on 12/Sep/21

$$yes.igotthesameanswer$$

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