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Category: Geometry

Question-208288

Question Number 208288 by efronzo1 last updated on 10/Jun/24 Answered by A5T last updated on 10/Jun/24 $$\mathrm{8}\left(\mathrm{8}+{x}\right)=\left(\mathrm{2}{r}\right)\left(\mathrm{2}{r}+\mathrm{2}{R}\right)=\mathrm{4}{r}^{\mathrm{2}} +\mathrm{4}{rR} \\ $$$$\Rightarrow{x}=\frac{{r}^{\mathrm{2}} +{rR}−\mathrm{16}}{\mathrm{2}}…\left({i}\right) \\ $$$$\left(\mathrm{8}+{x}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} +\left(\mathrm{2}{r}+{R}\right)^{\mathrm{2}}…

X-Y-and-Z-are-points-on-the-sides-AB-BC-and-AC-of-the-triangle-ABC-such-that-AX-XB-4-3-BY-YC-2-3-CZ-ZA-2-1-Find-the-ratio-of-the-area-of-the-triangle-XYZ-to-that-of-triangle-ABC-

Question Number 208158 by necx122 last updated on 06/Jun/24 $${X},\:{Y}\:{and}\:{Z}\:{are}\:{points}\:{on}\:{the}\:{sides}\:{AB}, \\ $$$${BC}\:{and}\:{AC}\:{of}\:{the}\:{triangle}\:{ABC},\:{such} \\ $$$${that}\:{AX}:{XB}\:=\mathrm{4}:\mathrm{3},\:{BY}:{YC}=\mathrm{2}:\mathrm{3},\: \\ $$$${CZ}:{ZA}=\mathrm{2}:\mathrm{1}.\:{Find}\:{the}\:{ratio}\:{of}\:{the}\:{area} \\ $$$${of}\:{the}\:{triangle}\:{XYZ}\:{to}\:{that}\:{of}\:{triangle} \\ $$$${ABC}. \\ $$ Answered by mr…