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Category: Geometry

Question-35798

Question Number 35798 by ajfour last updated on 23/May/18 Commented by ajfour last updated on 23/May/18 $$\bigtriangleup{ABC}\:{and}\:\bigtriangleup{CDE}\:{are}\:{congruent}. \\ $$$${Find}\:{the}\:{area}\:{of}\:{quadrilateral} \\ $$$${APQC}\:{in}\:{terms}\:{of}\:{a},\:{b},\:{and}\:{c}\:;\:{the} \\ $$$${sides}\:{of}\:\bigtriangleup{ABC}\:. \\ $$…

Question-166861

Question Number 166861 by Tawa11 last updated on 01/Mar/22 Commented by cortano1 last updated on 01/Mar/22 $$\Rightarrow\mathrm{3}.\mathrm{x}=\mathrm{6}.\mathrm{2}\Rightarrow\mathrm{x}=\mathrm{4} \\ $$$$\Rightarrow\mathrm{r}=\sqrt{\mathrm{2}^{\mathrm{2}} +\mathrm{6}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} }\:=\sqrt{\mathrm{49}+\mathrm{16}}=\sqrt{\mathrm{65}} \\ $$…

Question-35763

Question Number 35763 by $@ty@m last updated on 23/May/18 Answered by ajfour last updated on 23/May/18 $${let}\:\angle{BDF}\:=\:\alpha \\ $$$${AF}=\mathrm{30cos}\:{A}\:\:;\:\:\:{AE}=\mathrm{36cos}\:{A} \\ $$$$\mathrm{cot}\:\alpha\:=\:\frac{{AF}\mathrm{cos}\:{B}+{AE}\mathrm{cos}\:{C}}{{BF}\mathrm{sin}\:{B}−{CE}\mathrm{sin}\:{C}} \\ $$$$\:\:\:=\frac{\mathrm{30cos}\:{A}\mathrm{cos}\:{B}+\mathrm{36cos}\:{A}\mathrm{cos}\:{C}}{\left(\mathrm{18}−\mathrm{30cos}\:{A}\right)\mathrm{sin}\:{B}−\left(\mathrm{15}−\mathrm{36cos}\:{A}\right)\mathrm{sin}\:{C}} \\ $$$${BD}={BF}\mathrm{cos}\:{B}+{BF}\mathrm{sin}\:{B}\mathrm{cot}\:\alpha…

Question-35750

Question Number 35750 by ajfour last updated on 23/May/18 Commented by ajfour last updated on 23/May/18 $${Find}\:{proportion}\:{of}\:{blue},\:{brown}, \\ $$$${yellow},\:{and}\:{red}\:{coloured}\:{areas}. \\ $$$${Given}:\:{chord}\:{makes}\:{angle}\:\theta\:{with} \\ $$$${the}\:{diameter}\:{shown}\:{and}\:{that}\:{the} \\ $$$${point}\:{of}\:{intersection}\:{of}\:{the}\:{chord}…