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Category: Geometry

Question-169572

Question Number 169572 by mnjuly1970 last updated on 03/May/22 Answered by mr W last updated on 03/May/22 $${EO}={OC}=\mathrm{1},\:{say} \\ $$$$\angle{HOC}=\angle{AOE}=\angle{B} \\ $$$${AE}=\mathrm{1}×\mathrm{tan}\:{B} \\ $$$$\mathrm{tan}\:{A}=\frac{{EC}}{{AE}}=\frac{\mathrm{2}}{\mathrm{1}×\mathrm{tan}\:{B}} \\…

given-that-the-parametric-equation-of-a-curvd-are-x-1-t-1-y-1-t-1-obtaun-a-cartesian-equation-of-the-curve-Hemce-find-an-equqtion-of-tbe-nirmal-to-the-curve-at-the-point-t-2-

Question Number 103751 by hardylanes last updated on 17/Jul/20 $$ \\ $$$${given}\:{that}\:{the}\:{parametric}\:{equation}\:{of}\: \\ $$$${a}\:{curvd}\:{are}\:{x}=\frac{\mathrm{1}}{{t}−\mathrm{1}}\:\:{y}=\frac{\mathrm{1}}{{t}+\mathrm{1}}\:{obtaun}\:{a}\: \\ $$$${cartesian}\:{equation}\:{of}\:{the}\:{curve}.\:{Hemce}\:{find} \\ $$$${an}\:{equqtion}\:{of}\:{tbe}\:{nirmal}\:{to}\:{the}\:{curve}\:{at}\:{the}\: \\ $$$${point}\:{t}=\mathrm{2} \\ $$ Answered by bobhans…

Question-169281

Question Number 169281 by mnjuly1970 last updated on 28/Apr/22 Commented by cortano1 last updated on 28/Apr/22 $$\mathrm{tan}\:\beta=\frac{\mathrm{1}}{\mathrm{5}},\:\mathrm{tan}\:\left(\alpha+\beta\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{tan}\:\alpha\:=\frac{\mathrm{3}}{\mathrm{11}} \\ $$$$\therefore\:\mathrm{tan}\:\left(\mathrm{45}°+\alpha\right).\mathrm{tan}\:\left(\mathrm{45}°−\beta\right)= \\ $$$$\:\frac{\mathrm{1}+\frac{\mathrm{3}}{\mathrm{11}}}{\mathrm{1}−\frac{\mathrm{3}}{\mathrm{11}}}\:.\frac{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{5}}}\:=\:\frac{\mathrm{14}}{\mathrm{8}}\:.\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{7}}{\mathrm{6}} \\ $$…

In-AB-C-m-b-2-m-c-2-5-m-a-2-prove-that-A-90-m-a-median-

Question Number 169101 by mnjuly1970 last updated on 24/Apr/22 $$ \\ $$$$\:\:\:\:\:\:{In}\:\:{A}\overset{\Delta} {{B}C}\::\:\:\:\:{m}_{{b}} ^{\:\mathrm{2}} \:+\:{m}_{{c}} ^{\:\mathrm{2}} =\:\mathrm{5}\:{m}_{{a}} ^{\:\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\::\:\:\:\overset{\:\:\wedge} {{A}}\:=\:\mathrm{90}^{\:°} \\ $$$$\:\:\:\:\:\:\:\:\:\:{m}_{{a}} :\:\:\left(\:{median}\:\right) \\…

Question-38032

Question Number 38032 by behi83417@gmail.com last updated on 20/Jun/18 Commented by behi83417@gmail.com last updated on 21/Jun/18 $$\boldsymbol{{in}}\:\boldsymbol{{triangle}}\:\boldsymbol{{A}}\overset{\blacktriangle} {\boldsymbol{{B}C}}:\angle\boldsymbol{{A}}=\mathrm{72}^{\bullet} ,\boldsymbol{{BC}}=\mathrm{10}. \\ $$$$\boldsymbol{{D}}\:\boldsymbol{{and}}\:\boldsymbol{{E}},\boldsymbol{{can}}\:\boldsymbol{{move}}\:\boldsymbol{{on}}\:\boldsymbol{{BC}},\boldsymbol{{but}}\:\boldsymbol{{such}} \\ $$$$\boldsymbol{{that}},\boldsymbol{{alwyes}}:\boldsymbol{{AD}}=\boldsymbol{{AE}}. \\ $$$$\left.\mathrm{1}\right)\boldsymbol{{evaluate}}\:\angle\boldsymbol{{DAE}},\boldsymbol{{when}}\:\boldsymbol{{area}}\:\boldsymbol{{of}}\:…