Category: Geometry

Question Number 170010 by mr W last updated on 13/May/22 Commented by mr W last updated on 13/May/22 $${Given}\:{a}\:{triangle}\:\Delta{ABC}\:{with}\:{sides} \\ $$$${a},{b},{c}. \\ $$$${Find}\:{the}\:{area}\:{of}\:{the}\:{inscribed}\:{triangle} \\ $$$${in}\:{terms}\:{of}\:{a},{b},{c},\theta.…

Question Number 104445 by ajfour last updated on 21/Jul/20 Commented by ajfour last updated on 21/Jul/20 $${The}\:{central}\:{circle}\:{has}\:{radius}\:{b}. \\ $$$${The}\:{three}\:{smallest}\:{circles}\:{have} \\ $$$${radii}\:{a},\:{wbile}\:{the}\:{outer}\:{circles} \\ $$$${have}\:{radii}\:{c}.\:{Find}\:{c}\:{in}\:{terms} \\ $$$${of}\:{b}\:{and}\:{a}\:{when}\:{it}\:{is}\:{in}\:{contact}…

Question Number 104390 by I want to learn more last updated on 21/Jul/20 Answered by som(math1967) last updated on 21/Jul/20 $$\frac{\mathrm{XP}}{\mathrm{PY}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\:\frac{\mathrm{XP}}{\mathrm{XY}}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\frac{\mathrm{Ar}\bigtriangleup\mathrm{XPQ}}{\mathrm{Ar}\bigtriangleup\mathrm{XYZ}}=\frac{\mathrm{4}}{\mathrm{25}}…

Question Number 38849 by behi83417@gmail.com last updated on 30/Jun/18 Commented by behi83417@gmail.com last updated on 30/Jun/18 $$\:\boldsymbol{{raw}}\:\boldsymbol{{idea}}\:\boldsymbol{{to}}\:\boldsymbol{{mr}}\:\boldsymbol{{Ajfour}}! \\ $$$$\boldsymbol{{a}}^{\mathrm{2}} =\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{t}}^{\mathrm{2}} \:\:,\boldsymbol{{z}}=\boldsymbol{{c}}.\boldsymbol{{cos}\theta} \\ $$$$\boldsymbol{{b}}^{\mathrm{2}} =\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 104364 by ajfour last updated on 21/Jul/20 Commented by ajfour last updated on 21/Jul/20 $${Find}\:{the}\:{area}\:{of}\:{the}\:\bigtriangleup{CGI}\:; \\ $$$${C}\:{is}\:{circumcentre}\:{of}\:\bigtriangleup{PQR}, \\ $$$${G}\:{its}\:{centroid}\:{and}\:{I}\:{its}\:{incentre}. \\ $$ Answered by…