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Category: Geometry

Question-166371

Question Number 166371 by behi834171 last updated on 19/Feb/22 Commented by mr W last updated on 19/Feb/22 $${i}\:{don}'{t}\:{think}\:{we}\:{can}\:{determine}\:{the} \\ $$$${angle}\:{only}\:{with}\:{the}\:{two}\:{given}\: \\ $$$${conditions},\:{see}\:{diagram}\:{below}.\:\: \\ $$ Commented…

Question-35279

Question Number 35279 by ajfour last updated on 17/May/18 Commented by ajfour last updated on 17/May/18 $${Given}\:{two}\:{circles}\:{of}\:{radii}\:\boldsymbol{{r}}\:{and}\:\boldsymbol{{R}}. \\ $$$${The}\:{circles}\:{touch}\:{each}\:{other} \\ $$$${internally}.\:{Triangle}\:{ABC}\:{has} \\ $$$${its}\:{vertex}\:\boldsymbol{{A}}\:{at}\:{the}\:{point}\:{where} \\ $$$${the}\:{circles}\:{touch}.\:{Vertex}\:\boldsymbol{{B}}\:{lies}…

Question-166252

Question Number 166252 by mr W last updated on 16/Feb/22 Commented by mr W last updated on 16/Feb/22 $${find}\:{the}\:{side}\:{length}\:{s}\:{of}\:{the}\:{maximum} \\ $$$${equilateral}\:{triangle}\:{inscribed} \\ $$$${between}\:{the}\:{parabolas}\:{y}={x}^{\mathrm{2}} \:{and}\:{x}={y}^{\mathrm{2}} .…

Question-35167

Question Number 35167 by behi83417@gmail.com last updated on 16/May/18 Commented by behi83417@gmail.com last updated on 16/May/18 $${refer}\:{to}\:{Q}#\mathrm{35115} \\ $$$${AM}={AN},{sin}\frac{{A}}{\mathrm{2}}=\frac{{MN}}{\mathrm{2}{AN}}\Rightarrow{MN}=\mathrm{2}{AN}.{sin}\frac{{A}}{\mathrm{2}} \\ $$$${AMON},{is}\:{cyclic},{so}: \\ $$$${AO}.{MN}={AM}.{ON}+{AN}.{OM}\Rightarrow \\ $$$$\mathrm{2}{r}.{AN}={AO}.\mathrm{2}{AN}.{sin}\frac{{A}}{\mathrm{2}}\Rightarrow{AO}=\frac{{r}}{{sin}\frac{{A}}{\mathrm{2}}}…