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 27422 by Rasheed.Sindhi last updated on 06/Jan/18

$$\mathrm{A},\mathrm{B},\mathrm{C}\mathrm{\&}\mathrm{D}\mathrm{are}\mathrm{four}\mathrm{distinct}\mathrm{points}$$$$\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{in}\mathrm{such}\mathrm{a}\mathrm{way}\mathrm{that}\mathrm{chords}$$$$\mathrm{AB}\mathrm{\&}\mathrm{CD}\mathrm{cut}\mathrm{each}\mathrm{other}\mathrm{inside}$$$$\mathrm{the}\mathrm{circle}\mathrm{at}\mathrm{the}\mathrm{point}\mathrm{E}.\mathrm{Consequently}$$$$\mathrm{the}\mathrm{circle}\mathrm{is}\mathrm{divided}\mathrm{in}\mathrm{four}\mathrm{parts}$$$$(\mathrm{AEC},\mathrm{CEB},\mathrm{BED}\mathrm{\&}\mathrm{DEA}).$$$$[\mathrm{AEC}\mathrm{means}\mathrm{the}\mathrm{region}\mathrm{outlined}$$$$\mathrm{by}\stackrel{⌢}{\mathrm{AC}},\overline{\mathrm{AE}}\mathrm{\&}\overline{\mathrm{CE}}]$$$$\mathrm{If}\mathrm{AE}:\mathrm{BE}=\mathrm{a}:\mathrm{b}\mathrm{and}\mathrm{CE}:\mathrm{DE}=\mathrm{c}:\mathrm{d},$$$$\mathrm{what}\mathrm{is}\mathrm{ratio}\mathrm{between}\mathrm{the}\mathrm{four}$$$$\mathrm{parts}\mathrm{of}\mathrm{the}\mathrm{circle}?$$

Commented by Rasheed.Sindhi last updated on 07/Jan/18

Commented by Rasheed.Sindhi last updated on 07/Jan/18

$$\mathrm{Is}\mathrm{the}\mathrm{data}\mathrm{sufficient}\mathrm{to}\mathrm{prove}$$$$\mathrm{the}\mathrm{result}?\mathrm{Perhaps}\mathrm{not}\mathrm{so}\mathrm{please}$$$$\mathrm{suppose}\mathrm{that}\mathrm{\angle }\mathrm{AEC}=\theta$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com