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Category: Geometry

all-square-is-a-rhombus-why-

Question Number 65189 by arcana last updated on 26/Jul/19 $${all}\:{square}\:{is}\:{a}\:{rhombus}.\:{why}? \\ $$ Answered by MJS last updated on 26/Jul/19 $$\mathrm{a}\:\mathrm{rhombus}\:\mathrm{has}\:\mathrm{2}\:\mathrm{parallel}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{sides},\:\mathrm{all} \\ $$$$\mathrm{of}\:\mathrm{them}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{length} \\ $$$$\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{a}\:\mathrm{special}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{rhombus} \\…

Question-64971

Question Number 64971 by Tawa1 last updated on 23/Jul/19 Commented by Tony Lin last updated on 23/Jul/19 $$\frac{\frac{{x}}{\mathrm{2}}}{{sin}\theta}=\frac{\frac{{x}}{\mathrm{2}}+\mathrm{1}}{{sin}\left(\mathrm{90}°+\theta\right)}=\frac{{x}}{{sin}\left(\mathrm{90}°−\mathrm{2}\theta\right)} \\ $$$$\Rightarrow\frac{\frac{{x}}{\mathrm{2}}}{{sin}\theta}=\frac{\frac{{x}}{\mathrm{2}}+\mathrm{1}}{{cos}\theta}=\frac{{x}}{{cos}\mathrm{2}\theta} \\ $$$${let}\:{cos}\theta={t} \\ $$$$\Rightarrow\frac{\frac{{x}}{\mathrm{2}}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\frac{\frac{{x}}{\mathrm{2}}+\mathrm{1}}{{t}}=\frac{{x}}{\mathrm{2}{t}^{\mathrm{2}}…

Question-64909

Question Number 64909 by Tawa1 last updated on 23/Jul/19 Commented by MJS last updated on 23/Jul/19 $$\mathrm{the}\:\mathrm{picture}\:\mathrm{shows}\:\mathrm{2}\:\mathrm{circles},\:\mathrm{so}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{numbers}\:\mathrm{don}'\mathrm{t}\:\mathrm{fit}.\:\mathrm{obviously}\:\mathrm{the}\:\mathrm{right}\:\mathrm{must} \\ $$$$\mathrm{be}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{the}\:\mathrm{above}/\mathrm{below}\:\mathrm{numbers} \\ $$ Commented by…