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Question Number 49360 by behi83417@gmail.com last updated on 06/Dec/18

Commented by behi83417@gmail.com last updated on 06/Dec/18

$$\mathbf{when}\mathbf{area}\mathbf{of}:AGEC,\mathbf{is}\mathbf{maximum},$$$$\mathbf{then}:\frac{\mathbf{GE}}{\mathbf{AC}}=?$$

Commented by MJS last updated on 06/Dec/18

$$\mathrm{I}\mathrm{think}\mathrm{if}\mathrm{you}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{fix}D\Rightarrow \mid AD\mid =\mathrm{\infty };AC\parallel GE$$$$\frac{GE}{AC}=\frac{1}{2}$$$$\mathrm{because}\mathrm{greatest}\mathrm{trapezoid}\mathrm{can}\mathrm{be}\mathrm{found}\mathrm{as}$$$$\mathrm{follows}:$$$$\frac{AC}{2}=r$$$$\frac{GE}{2}=r\cos \alpha$$$$h=r\sin \alpha$$$$\mathrm{area}\left(ACEG\right)=r^2(1+\cos \alpha )\sin \alpha$$$$\frac{d}{d\alpha }\left[r^2(1+\cos \alpha )\sin \alpha \right]=0$$$$r^2({2\cos }^2\alpha +\cos \alpha -1)=0$$$$\cos \alpha =\frac{1}{2}\Rightarrow \frac{GE}{AC}=\frac{1}{2}$$

Commented by behi83417@gmail.com last updated on 06/Dec/18

$$thankyousirforattention.thisismy$$$$typo.excuseme.$$$$yes,\mathbf{D}isafixpoint.$$

Commented by peter frank last updated on 06/Dec/18

$$\mathrm{sir}\mathrm{plz}\mathrm{check}\mathrm{QN}49357,49358$$

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