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Question Number 39104 by behi83417@gmail.com last updated on 02/Jul/18

Commented by behi83417@gmail.com last updated on 02/Jul/18

$$\stackrel{\wedge }{\mathit{B}}={100}^{\bullet },\mathit{A}\mathit{C}=10,\mathit{A}\mathit{D}=\mathit{D}\mathit{B}=\mathit{B}\mathit{E}=\mathit{E}\mathit{C}.$$$$\Rightarrow \measuredangle \mathit{D}\mathit{B}\mathit{E}=?,\mathit{D}\mathit{E}=?$$$$(\mathit{i}\mathit{s}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{e}\mathit{a}\mathit{d}\mathit{d}\mathit{i}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{a}\mathit{l}\mathit{c}\mathit{o}\mathit{n}\mathit{d}\mathit{i}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{s}$$$$\mathit{n}\mathit{e}\mathit{e}\mathit{d}\mathit{e}\mathit{d}?)$$

Answered by MrW3 last updated on 02/Jul/18

$$let\alpha =\mathrm{\angle }A$$$$\mathrm{\angle }BDE=2\alpha$$$$\mathrm{\angle }DBE=180°-4\alpha >0\Rightarrow \alpha <45°$$$$\mathrm{\angle }B=2\alpha +180°-4\alpha =72°(!!)$$$$\Rightarrow 2\alpha =180°-72°=104°$$$$\Rightarrow \alpha =52°>45°$$$$\Rightarrow Geometrynotpossible!$$$$\mathrm{\angle }B=72°istoosmall!$$$$$$$${let}^{\prime }sassume\mathrm{\angle }B=100°$$$$\Rightarrow \alpha =\frac{180°-100°}{2}=40°$$$$\mathrm{\angle }DBE=180°-4\times 40°=20°$$$$letAD=DB=BE=EC=k$$$$2(k+k\sin \frac{20°}{2})=AC=10$$$$\Rightarrow k=\frac{10}{2(1+\sin 10°)}=4.26$$$$DE=2k\sin \frac{20°}{2}=1.5$$

Commented by behi83417@gmail.com last updated on 02/Jul/18

$$thanksinadvancedearmaster.$$$$conditionsfixed.$$

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