Question Number 68930 by Maclaurin Stickker last updated on 17/Sep/19 $$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{we}\:\mathrm{have}\:\mathrm{7}\:\mathrm{circles}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{radius}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{and}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gray}\:\mathrm{region}. \\ $$ Commented by Maclaurin Stickker last updated…
Question Number 134428 by liberty last updated on 03/Mar/21 $$\mathrm{In}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{4}\:\mathrm{cm}.\:\mathrm{Point}\:\mathrm{Q}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{middle}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{point}\:\mathrm{P} \\ $$$$\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{extension}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AB} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{BP}\::\:\mathrm{AB}\:=\:\mathrm{1}\::\:\mathrm{2}.\:\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{QG}\:\mathrm{line}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{PQH}\:\mathrm{plane}\:,\:\mathrm{then}\:\mathrm{sin}\:\theta\:=?\: \\ $$ Answered…
Question Number 3348 by RasheedSindhi last updated on 11/Dec/15 $${Prove}\:{that}\:{the}\:{regular}\:{pentagon} \\ $$$${is}\:{possible}\:{with}\:{ruler}\:{and}\:{compass}. \\ $$ Commented by Rasheed Soomro last updated on 11/Dec/15 $$\mathcal{H}{ow}\:{can}\:{we}\:{prove}\:{that}\:{angle}\:\mathrm{108}°\:{is} \\ $$$${possible}?…
Question Number 134396 by I want to learn more last updated on 03/Mar/21 Commented by mr W last updated on 03/Mar/21 $${P}+{Q}=\mathrm{2}×\mathrm{10}×\mathrm{sin}\:\frac{\mathrm{75}°}{\mathrm{2}}=\mathrm{12}.\mathrm{2}\:{unit} \\ $$ Commented…
Question Number 3304 by prakash jain last updated on 09/Dec/15 $$\mathrm{Bring}\:\mathrm{up}\:\mathrm{the}\:\mathrm{topic}/\mathrm{challenge}\:\mathrm{started}\:\mathrm{by}\:\mathrm{Filup}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}. \\ $$$$\mathrm{Shall}\:\mathrm{we}\:\mathrm{start}\:\mathrm{new}\:\mathrm{topic}\:\mathrm{at}\:\mathrm{the}\:\mathrm{beginning} \\ $$$$\mathrm{of}\:\mathrm{calendar}\:\mathrm{month}? \\ $$$$\mathrm{See}\:\mathrm{older}\:\mathrm{post}\:\mathrm{dt}\:\mathrm{24}.\mathrm{11}\:\mathrm{by}\:\mathrm{Filup} \\ $$ Commented by Filup last updated on…
Question Number 68831 by Maclaurin Stickker last updated on 15/Sep/19 $$\mathrm{The}\:\mathrm{square}\:{ABCD}\:\mathrm{has}\:\mathrm{side}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:{AP}\:\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{8}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:{PMN}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{square}. \\ $$ Commented by Maclaurin Stickker last updated…
Question Number 3280 by Filup last updated on 09/Dec/15 $$\mathrm{For}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{perpandicular} \\ $$$$\mathrm{height}\:{h}\:\mathrm{and}\:\mathrm{base}\:\mathrm{length}\:{b},\:\mathrm{the}\: \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$${A}=\frac{\mathrm{1}}{\mathrm{2}}{hb} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{the}\:\mathrm{case}? \\ $$$$\mathrm{I}\:\mathrm{understand}\:\mathrm{that}\:\mathrm{two}\:\mathrm{identicle}\:\mathrm{triangles} \\ $$$$\mathrm{can}\:\mathrm{construct}\:\mathrm{a}\:{rectangle},\:\mathrm{so}\:\mathrm{the}\:\mathrm{area} \\…
Question Number 3262 by Rasheed Soomro last updated on 08/Dec/15 $$\mathcal{C}{ould}\:\:^{\mathrm{3}} \sqrt{\mathrm{2}}\:\:{be}\:{drawn}\:{on}\:{numbered}\:{line}\:{with}\: \\ $$$${the}\:{help}\:\:{of}\:\:{ruler}\:{and}\:{compass}\:{only}? \\ $$ Commented by prakash jain last updated on 09/Dec/15 $$\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{drawn}\:\mathrm{using}\:\mathrm{a}\:\mathrm{ruler}\:\mathrm{and}\:\mathrm{compass}.…
Question Number 3249 by Rasheed Soomro last updated on 08/Dec/15 $$\mathcal{H}{ow}\:{could}\:\sqrt{\mathrm{5}}\:\:{be}\:{drawn}\:{on}\:{numbered}\:{line}\:{using} \\ $$$${scale}\:{and}\:{compass}\:{only}?\:\left({Exactly}\:\sqrt{\mathrm{5}}\:{not}\:{its}\:{decimal}\:{approximation}.\right) \\ $$ Answered by prakash jain last updated on 08/Dec/15 $$\mathrm{For}\:\sqrt{\mathrm{5}} \\…
Question Number 68666 by ahmadshah last updated on 14/Sep/19 Commented by mr W last updated on 14/Sep/19 Commented by mr W last updated on 14/Sep/19…