Question Number 3830 by Rasheed Soomro last updated on 21/Dec/15 $$\mathcal{D}{raw}\:{a}\:{rectangle}\:{of}\:{maximum}\:{perimeter}, \\ $$$${by}\:{ruler}\:{and}\:{compass},{when}\:{area}\:{is}\:\boldsymbol{\mathrm{ab}}.\: \\ $$$$\left(\boldsymbol{\mathrm{AB}}\:=\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{CD}}=\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{given}}.\right) \\ $$ Commented by prakash jain last updated on 22/Dec/15…
Question Number 3823 by Rasheed Soomro last updated on 21/Dec/15 $${Consider}\:{a}\:{triangle}\:\mathrm{ABC}.\:{Let}\:\mathrm{D}\:\:{and}\:\:\mathrm{E} \\ $$$${are}\:{two}\:{points}\:{on}\:\mathrm{AB}\:\:{and}\:\:\mathrm{AC}\:{respectively} \\ $$$${such}\:{that}\:\mathrm{DE}\:\parallel\:\mathrm{BC}.\:{Now}\:{there}\:{are}\:{two} \\ $$$${parts}\:{of}\:\bigtriangleup\mathrm{ABC}\::\:\bigtriangleup\mathrm{ADE}\:\:\:{and}\:\:{trapizoid} \\ $$$$\mathrm{DBCE}.\:{If}\:{these}\:{two}\:{regions}\:{have}\:{same}\:{area} \\ $$$${What}\:{will}\:{be}\:{the}\:{ratio}\:{of}\:{two}\:{distances}\:: \\ $$$$\left({i}\right)\:{distance}\:{of}\:\mathrm{DE}\:{from}\:{point}\:\mathrm{A}\:{and} \\ $$$$\left({ii}\right)\:{distance}\:{between}\:\mathrm{BC}\:{and}\:\mathrm{DE}\:\:?…
Question Number 3808 by Rasheed Soomro last updated on 21/Dec/15 $${A}\:{chord}\:{divides}\:\:{the}\:{circle}\:{in}\:{two} \\ $$$${segments},{having}\:{areas}\:{s}_{\mathrm{1}} \:{and}\:\:{s}_{\mathrm{2}} . \\ $$$${If}\:{diameter},\:{perpendicular}\:{to}\:{this} \\ $$$${chord}\:{is}\:{cut}\:{into}\:\mathrm{1}:\mathrm{3}\:{by}\:{the}\:{chord}\:,{what}\:{is}\:{s}_{\mathrm{1}} :{s}_{\mathrm{2}} \:? \\ $$$$ \\ $$…
Question Number 69272 by TawaTawa last updated on 22/Sep/19 Answered by $@ty@m123 last updated on 22/Sep/19 $${Let}\:\angle{DPC}=\theta \\ $$$$\Rightarrow\angle{Q}=\theta−\mathrm{30} \\ $$$${Let}\:{CP}={x} \\ $$$${In}\:\bigtriangleup{DCP}, \\ $$$$\mathrm{tan}\:\theta=\frac{\sqrt{\mathrm{3}}}{{x}}\:…\left(\mathrm{1}\right)…
Question Number 3714 by Rasheed Soomro last updated on 19/Dec/15 $$\mathcal{D}\mathrm{erive}\:\mathrm{a}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{volume}\:\mathrm{of}\:\boldsymbol{\mathrm{right}}\:\boldsymbol{\mathrm{circular}}\:\boldsymbol{\mathrm{cone}} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{volume}\:\mathrm{of}\:\boldsymbol{\mathrm{cyllinder}}\:\:\mathrm{is}\:\mathrm{given}. \\ $$ Answered by Filup last updated on 19/Dec/15 $$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{how}\:\mathrm{to}\:\mathrm{answer}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{given}.\:\mathrm{But}\:\mathrm{I}\:\mathrm{can}\:\mathrm{show}\:\mathrm{it}\:\mathrm{this}\:\mathrm{way}:…
Question Number 134772 by bramlexs22 last updated on 07/Mar/21 $$ \\ $$What is the equation of a circle that goes through points (0,1), (1,4), and…
Question Number 3695 by Rasheed Soomro last updated on 19/Dec/15 $$\mathcal{C}{an}\:{we}\:{say}\:{that} \\ $$$$\mathcal{A}\:{line}\:{is}\:{a}\:{circle}\:{whose}\:{radius}\:{is}\:\infty \\ $$$$\mathcal{O}{r} \\ $$$${A}\:{circle}\:{with}\:\infty\:{radius}\:{is}\:{a}\:{line}\:\:? \\ $$ Commented by Filup last updated on…
Question Number 3662 by Filup last updated on 18/Dec/15 $$\mathrm{Lets}\:\mathrm{say}\:\mathrm{we}\:\mathrm{have}\:\mathrm{an}\:{n}−\mathrm{gon}. \\ $$$$\mathrm{All}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{equal}. \\ $$$$ \\ $$$$\mathrm{When}\:{n}=\mathrm{3},\:\mathrm{interior}\:\mathrm{angles}\:\theta=\frac{\mathrm{180}}{\mathrm{3}} \\ $$$$\theta=\mathrm{60}° \\ $$$$ \\ $$$${n}=\mathrm{4},\:\theta=\frac{\mathrm{360}}{\mathrm{4}}=\mathrm{90}° \\ $$$$\vdots \\…
Question Number 69192 by TawaTawa last updated on 21/Sep/19 Answered by mr W last updated on 21/Sep/19 $${let}\:\angle{BAD}=\alpha \\ $$$${side}\:{length}\:={a} \\ $$$$\frac{{a}}{\mathrm{sin}\:\left(\mathrm{60}+\alpha\right)}=\frac{\mathrm{3}}{\mathrm{sin}\:\alpha}\:\:\:\:…\left({i}\right) \\ $$$$\frac{{a}}{\mathrm{sin}\:\left(\mathrm{60}+\mathrm{30}−\alpha\right)}=\frac{{a}}{\mathrm{cos}\:\alpha}=\frac{\mathrm{5}}{\mathrm{sin}\:\left(\mathrm{30}−\alpha\right)}\:\:\:…\left({ii}\right) \\…
Question Number 3647 by Rasheed Soomro last updated on 17/Dec/15 $${Draw}\:{a}\:{line}\:{segment}\:{equal}\:{to} \\ $$$$\boldsymbol{{ab}}\:{units}\:{when}\:{AB}=\boldsymbol{{a}}\:{units}\:\:{and}\:{CD}=\boldsymbol{{b}}\:{units}\: \\ $$$${are}\:{given}.\:{Only}\:{ruler}\:{and}\:{compass}\:{may}\:{be} \\ $$$${used}. \\ $$ Commented by prakash jain last updated…