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Question Number 80119 by M±th+et£s last updated on 31/Jan/20

Answered by key of knowledge last updated on 31/Jan/20

$$\hat{\mathrm{C}}=108\Rightarrow \mathrm{CD}=\mathrm{CB}\Rightarrow \mathrm{C}\widehat{\mathrm{B}D}=36$$$$\mathrm{D}\widehat{\mathrm{B}F}=\mathrm{F}\widehat{\mathrm{B}A}=\frac{108-36}{2}=36$$$$\mathrm{F}\widehat{\mathrm{B}A}=\frac{\mathrm{F}\stackrel{⌢}{\mathrm{A}}}{2}=36\Rightarrow \stackrel{⌢}{\mathrm{F}A}=72\left(\mathrm{i}\right)$$$$\mathrm{A}\stackrel{⌢}{\mathrm{E}}=\frac{360}{5}=36\left(\mathrm{ii}\right)\Rightarrow \mathrm{i},\mathrm{ii}\Rightarrow \mathrm{E}=\mathrm{F}\Rightarrow \mathrm{EF}=0$$$$\frac{\mathrm{CF}}{\mathrm{AF}}=\frac{\mathrm{CE}}{\mathrm{AE}}=\frac{\mathrm{a}}{\sqrt{{2\mathrm{a}}^2-{2\mathrm{a}}^2\cos 108}}\ne 2$$

Answered by mr W last updated on 31/Jan/20

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