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Category: Geometry

Question-45630

Question Number 45630 by ajfour last updated on 14/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/Oct/18 $$\frac{\mathrm{1}}{\mathrm{2}}×{l}×{x}=\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}\: \\ $$$${s}=\frac{{R}+{x}+{x}+{r}+{l}}{\mathrm{2}}={x}+\frac{{R}+{r}+{l}}{\mathrm{2}} \\ $$$${a}={R}+{x}\:\:\:\:{b}={x}+{r}\:\:\:\:{c}={l} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{lx}=\sqrt{\left({x}+\frac{{R}+{r}+{l}}{\mathrm{2}}\right)\left(\frac{{r}+{l}+{R}}{\mathrm{2}}−{R}\right)\left(\frac{{R}+{l}+{r}}{\mathrm{2}}−{r}\right)\left({x}+\frac{{R}+{r}+{l}}{\mathrm{2}}−{l}\right)}\: \\ $$$$\frac{{l}^{\mathrm{2}}…

Question-45448

Question Number 45448 by MrW3 last updated on 13/Oct/18 Commented by MrW3 last updated on 13/Oct/18 $${When}\:{an}\:{ellipse}\:{is}\:{rotated}\:{by}\:{an} \\ $$$${angle}\:\alpha,\:{the}\:{five}\:{partial}\:{areas}\:{are}\:{equal}. \\ $$$${Find}\:{the}\:{equation}\:{of}\:{the}\:{ellipse} \\ $$$${for}\:\alpha=\mathrm{90}°\:{and}\:\mathrm{45}°\:{respectively}. \\ $$…

Question-45381

Question Number 45381 by behi83417@gmail.com last updated on 12/Oct/18 Commented by behi83417@gmail.com last updated on 12/Oct/18 $$\angle{ABN}=\angle{NBO}=\angle{OBC}=\frac{\angle{ABC}}{\mathrm{3}} \\ $$$$\angle{BAN}=\angle{NAC},\angle{ACO}=\angle{OCB} \\ $$$${AB}=\mathrm{12},{BC}=\mathrm{8},{AC}=\mathrm{10} \\ $$$${Q}#\mathrm{1}={radius}\:{of}\:{red}\:\:{circle}. \\ $$$${Q}#\mathrm{2}={area}\:{of}\:\:{N}\overset{\lozenge}…