Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 174763 by dragan91 last updated on 10/Aug/22

Answered by a.lgnaoui last updated on 11/Aug/22

$$\mathrm{\angle }ADF$$$$\frac{\sin \mathrm{A}}{\mathrm{DF}}=\frac{\sin \mathrm{F}}{\mathrm{AD}}=\frac{\sin \mathrm{D}}{24}\left(1\right)$$$$\mathrm{\angle }EBF$$$$\frac{\sin \mathrm{B}}{\mathrm{x}}=\frac{\sin \mathrm{F}}{3}=\frac{\sin \mathrm{E}}{8}\left(2\right)$$$$\mathrm{\angle }CDE$$$$\frac{\sin \mathrm{D}}{3}=\frac{\sin \mathrm{C}}{\mathrm{DE}}=\frac{\sin \mathrm{E}}{\mathrm{CD}}\left(3\right)$$$$\left(2\right)\mathrm{and}\left(3\right)$$$$\frac{\sin \mathrm{E}}{8}=\frac{\sin \mathrm{F}}{3}\sin \mathrm{E}=8\frac{\sin \mathrm{F}}{3}$$$$\frac{\sin \mathrm{E}}{\mathrm{CD}}=\frac{\sin \mathrm{D}}{3}\sin \mathrm{E}=\frac{\mathrm{CDsin}\mathrm{D}}{3}$$$$\frac{8\sin \mathrm{F}}{3}=\frac{\mathrm{CDsin}\mathrm{D}}{3}\mathrm{CD}=\frac{8\sin \mathrm{F}}{\sin \mathrm{D}}$$$$\mathrm{\angle }ADF\frac{\sin \mathrm{F}}{\mathrm{AD}}=\frac{\sin \mathrm{D}}{24}\Rightarrow \frac{\sin \mathrm{F}}{\sin \mathrm{D}}=\frac{\mathrm{AD}}{24}$$$$\mathrm{CD}=8\frac{\mathrm{AD}}{24},\mathrm{CD}=\frac{\mathrm{AD}}{3}\Rightarrow \mathrm{AC}=4\mathrm{CD}$$$$\frac{\mathrm{CD}}{\mathrm{CI}}=\frac{\mathrm{CE}}{\mathrm{BC}}=\frac{1}{2}=\frac{\mathrm{DE}}{\mathrm{BI}}(\mathrm{DE}\parallel \mathrm{BI})$$$$\mathrm{GD}\mid \mid \mathrm{BC}\frac{\mathrm{FE}}{\mathrm{FD}}=\frac{\mathrm{FB}}{\mathrm{FG}}\Rightarrow \frac{\mathrm{x}}{\mathrm{FD}}=\frac{8}{12}=\frac{2}{3}$$$$\mathrm{H}\in \mathrm{EF}(\mathrm{BH}\mid \mid \mathrm{AC})\measuredangle DCB=\measuredangle CBH$$$$\measuredangle C+\measuredangle D=\measuredangle B+\measuredangle FCE=BE\Rightarrow DE=EH=3\measuredangle HBF=\measuredangle ACD=BH$$$$EF=2\times 3=6\Rightarrow \mathrm{x}=6$$

Commented by Tawa11 last updated on 11/Aug/22

$$\mathrm{Great}\mathrm{sir}$$

Answered by a.lgnaoui last updated on 11/Aug/22

Terms of Service

Privacy Policy

Contact: info@tinkutara.com