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Category: Geometry

Question-204944

Question Number 204944 by mr W last updated on 02/Mar/24 Commented by mr W last updated on 03/Mar/24 $${the}\:{distances}\:{from}\:{a}\:{point}\:{inside} \\ $$$${a}\:{triangle}\:{to}\:{its}\:{vertexes}\:{are}\:{p},\:{q},\:{r} \\ $$$${respectively}.\:{find}\:{the}\:{maximum} \\ $$$${area}\:{of}\:{the}\:{triangle}\:{and}\:{its}\:{sides}.…

The-figure-below-represents-a-design-on-the-windows-of-a-building-The-curved-part-XY-is-an-arc-of-a-circle-The-rise-of-the-segmental-arc-is-10cm-its-span-is-100cm-and-XZ-ZY-120cm-calculate-i-th

Question Number 204873 by necx122 last updated on 29/Feb/24 $${The}\:{figure}\:{below}\:{represents}\:{a}\:{design} \\ $$$${on}\:{the}\:{windows}\:{of}\:{a}\:{building}.\:{The} \\ $$$${curved}\:{part}\:{XY}\:{is}\:{an}\:{arc}\:{of}\:{a}\:{circle}. \\ $$$${The}\:{rise}\:{of}\:{the}\:{segmental}\:{arc}\:{is}\:\mathrm{10}{cm}, \\ $$$${its}\:{span}\:{is}\:\mathrm{100}{cm}\:{and}\:{XZ}={ZY}=\mathrm{120}{cm}. \\ $$$${calculate}: \\ $$$$\left({i}\right)\:{the}\:{radius}\:{of}\:{the}\:{circle} \\ $$$$\left({ii}\right)\:{the}\:{area}\:{of}\:{the}\:{segmental}\:{cap}, \\…

Question-204505

Question Number 204505 by cherokeesay last updated on 19/Feb/24 Answered by mr W last updated on 19/Feb/24 $$\left[\sqrt{\left(\mathrm{2}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} }−\mathrm{1}\right]^{\mathrm{2}} +\left(\mathrm{1}−{r}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\left[\mathrm{2}\sqrt{\mathrm{1}−{r}}−\mathrm{1}\right]^{\mathrm{2}} =\mathrm{2}{r}−\mathrm{1}…

Question-204374

Question Number 204374 by mr W last updated on 14/Feb/24 Commented by mr W last updated on 15/Feb/24 $${The}\:{radius}\:{of}\:{the}\:{big}\:{sphere}\:\left({say}\:\right. \\ $$$$\left.{the}\:{Earth}\right)\:{is}\:{R}\:{and}\:{the}\:{radius}\:{of} \\ $$$${the}\:{small}\:{sphere}\:\left({say}\:{theMoon}\right)\:{is}\:{r}. \\ $$$${find}\:{the}\:{maximum}\:{area}\:{of}\:{the}…