Menu Close

Category: Geometry

Question-187274

Question Number 187274 by normans last updated on 15/Feb/23 Commented by normans last updated on 15/Feb/23 $${suppose}\:{point}\:\boldsymbol{{P}}\:{are}\:{in}\:\bigtriangleup\boldsymbol{{ABC}} \\ $$$${then}\:{the}\:{bisector}\:\angle\boldsymbol{{BPC}},\angle\boldsymbol{{CPA}},\:\angle\boldsymbol{{APB}} \\ $$$${cut}\:{the}\:{sides}\:\boldsymbol{{BC}},\boldsymbol{{CA}}\:{and}\:\boldsymbol{{AB}}\:\:{each}\:{on}\:{point}\:\boldsymbol{{X}},\boldsymbol{{Y}}\:{and}\:\boldsymbol{{Z}}. \\ $$$${show}\:{that}\:\boldsymbol{{AX}},\boldsymbol{{BY}}\:\:{and}\:\boldsymbol{{CY}}\:{is}\:{a}\:{kongruen}. \\ $$$$…

Question-121615

Question Number 121615 by ajfour last updated on 10/Nov/20 Commented by ajfour last updated on 10/Nov/20 $${The}\:{blue}\:{triangle}\:{is}\:{right}\:{angled}\:{and} \\ $$$${isosceles}\:{with}\:\:{AF}={BF}=\mathrm{3}. \\ $$$${Radius}\:{of}\:{circle}\:{r}=\mathrm{2}. \\ $$$${Find}\:{maximum}\:{side}\:{length}\:{of} \\ $$$${equilateral}\:\bigtriangleup{DEF}.…

Question-187146

Question Number 187146 by Rupesh123 last updated on 14/Feb/23 Answered by a.lgnaoui last updated on 14/Feb/23 $$\bigtriangleup{SMI}\:\:{et}\:{RNI}\:{semblables}\:\:\: \\ $$$${I}\:{centre}\:{de}\:{SRMN}\:\:{SK}=\frac{{PQ}}{\mathrm{2}}=\mathrm{3} \\ $$$$\bigtriangleup{BRQ}\:\:\:{RIO}\:\:{Semblables} \\ $$$$\frac{{OR}}{{OI}}=\frac{\frac{{RN}}{\mathrm{2}}}{{HQ}}=\frac{{RQ}}{{BQ}}\Rightarrow\:\:\:\frac{{RN}}{\mathrm{2}{HQ}}=\frac{{RQ}}{{BQ}} \\ $$$${HQ}=\mathrm{3}\:\:{RQ}=\mathrm{6}\:\:\:{BQ}={BP}+\mathrm{6}…

Question-187100

Question Number 187100 by Tons last updated on 13/Feb/23 Answered by a.lgnaoui last updated on 14/Feb/23 $$\bigtriangleup{APB}\:\:\:\:{AB}\mathrm{sin}\:{X}={AC}\mathrm{cos}\:{Y}\:\: \\ $$$$ \\ $$$$\:{BC}=\mathrm{2}{AB}\mathrm{cos}\:{Y}\:\:\Rightarrow\begin{cases}{{Y}=\frac{\pi}{\mathrm{2}}−{X}}\\{{AB}={AC}}\end{cases} \\ $$$$\mathrm{sin}\:{X}=\mathrm{cos}\:{Y}\:\:\: \\ $$$$\bigtriangleup{ABCD}\:\:\:\:{Sqart}\left({Care}\right)…