Category: Geometry

Question Number 82378 by ajfour last updated on 20/Feb/20 Commented by ajfour last updated on 20/Feb/20 $$\mathrm{If}\mathrm{all}5\mathrm{regions}\mathrm{have}\mathrm{equal}\mathrm{areas},$$$$\mathrm{find}\mathrm{sides}\mathrm{of}\mathrm{rectangle},\mathrm{given}$$$$\mathrm{radius}=1.$$ Answered by…

Question Number 16771 by Tinkutara last updated on 26/Jun/17 Commented by Tinkutara last updated on 26/Jun/17 $$\left(1\right)O\mathrm{is}\mathrm{circumcenter}\mathrm{and}H\mathrm{is}\mathrm{orthocenter}$$$$\mathrm{of}\mathrm{\Delta }ABC.{AOA}^{\prime }\mathrm{is}\mathrm{the}\mathrm{diameter}.$$$$\mathrm{Prove}\mathrm{that}{A}^{\prime }BHC\mathrm{is}\mathrm{a}\mathrm{parallelogram}.$$ Answered by…

Question Number 16785 by RasheedSoomro last updated on 26/Jun/17 Commented by RasheedSoomro last updated on 26/Jun/17 $$\mathrm{Without}\mathrm{using}\mathrm{area}-\mathrm{formula}\mathrm{find}\mathrm{out}$$$$\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{shaded}\mathrm{part}\mathrm{to}\mathrm{the}\mathrm{whole}.$$ Commented by mrW1 last…

Question Number 16756 by Tinkutara last updated on 26/Jun/17 $$\mathrm{Alternate}\mathrm{vertices}\mathrm{of}\mathrm{a}\mathrm{regular}\mathrm{hexagon}$$$$\mathrm{are}\mathrm{joined}\mathrm{as}\mathrm{shown}.\mathrm{What}\mathrm{fraction}\mathrm{of}$$$$\mathrm{the}\mathrm{total}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{hexagon}\mathrm{is}$$$$\mathrm{shaded}?(\mathrm{Justify}\mathrm{your}\mathrm{answer}.)$$ Commented by Tinkutara last updated on 26/Jun/17…

Question Number 16740 by Tinkutara last updated on 26/Jun/17 $$\mathrm{The}\mathrm{maximum}\mathrm{value}\mathrm{of}$$$${\cos }^2\left(\cos (33\pi +\theta )\right)+{\sin }^2\left(\sin (45\pi +\theta )\right)$$$$\mathrm{is}$$$$\left(1\right)1+{\sin }^{2}1$$$$\left(2\right)2$$$$\left(\mathrm{3}\right)\:\mathrm{1}\:+\:\mathrm{cos}^{\mathrm{2}} \mathrm{1} \…