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Category: Geometry

Question-187893

Question Number 187893 by Rupesh123 last updated on 23/Feb/23 Answered by a.lgnaoui last updated on 23/Feb/23 $$\bigtriangleup{ABD}\:\:\:\:\frac{\mathrm{sin}\:\mathrm{53}}{{AD}}=\frac{\mathrm{sin}\:\left(\mathrm{14}+{x}\right)}{{AB}}=\frac{\mathrm{sin}\:\left(\mathrm{14}+\mathrm{53}+{x}\right)}{\mathrm{2}{k}} \\ $$$$\:\:\:\mathrm{2}{k}\mathrm{sin}\:\mathrm{53}={AD}\mathrm{sin}\:\left(\mathrm{67}+{x}\right)\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\bigtriangleup{ACD}\:\:\:\frac{\mathrm{sin}\:\mathrm{14}}{{k}}=\frac{\mathrm{sin}\:{x}}{{AD}} \\ $$$$\:\:\:\:\:{k}\mathrm{sin}\:{x}={AD}\mathrm{sin}\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$…

Question-187808

Question Number 187808 by LowLevelLump last updated on 22/Feb/23 Answered by a.lgnaoui last updated on 22/Feb/23 $$\bigtriangleup{ABC}'\:\:\begin{cases}{{AB}={AC}={BC}={a}}\\{{S}_{\mathrm{1}} =\frac{{a}^{\mathrm{2}} \sqrt{\mathrm{3}}}{\mathrm{2}}}\end{cases} \\ $$$$\bigtriangleup{ACB}'\:\:\:\begin{cases}{{AC}={AB}'={CB}'={b}}\\{{S}_{\mathrm{2}} =\frac{{b}^{\mathrm{2}} \sqrt{\mathrm{3}}}{\mathrm{2}}}\end{cases} \\ $$$$\bigtriangleup{BCC}'\:\:\:\begin{cases}{{BC}={BC}'={CC}^{'}…

Question-187765

Question Number 187765 by Tawa11 last updated on 21/Feb/23 Answered by cortano12 last updated on 21/Feb/23 $$\left(\mathrm{1i}\right)\Rightarrow\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)+\left(\mathrm{y}−\mathrm{3}\right)\left(\mathrm{y}−\mathrm{7}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{4x}−\mathrm{10y}+\mathrm{24}=\mathrm{0} \\ $$ Answered by…

if-point-P-is-any-point-inside-ABC-with-side-lenghts-a-b-and-c-prove-that-PA-a-PB-b-PC-c-3-

Question Number 187762 by normans last updated on 21/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\boldsymbol{{if}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\:\:\boldsymbol{{is}}\:\boldsymbol{{any}}\:\boldsymbol{{point}}\:\boldsymbol{{inside}}\:\:\: \\ $$$$\:\:\:\:\:\:\:\bigtriangleup\boldsymbol{{ABC}}\:\:\boldsymbol{{with}}\:\boldsymbol{{side}}\:\boldsymbol{{lenghts}}\:\boldsymbol{{a}},\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}.\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{PA}}}{\boldsymbol{{a}}}\:+\:\frac{\boldsymbol{{PB}}}{\boldsymbol{{b}}}\:+\:\frac{\boldsymbol{{PC}}}{\boldsymbol{{c}}}\:\geqslant\:\sqrt{\mathrm{3}\:} \\ $$$$ \\ $$ Terms of Service…