Question Number 46906 by behi83417@gmail.com last updated on 02/Nov/18 Commented by behi83417@gmail.com last updated on 03/Nov/18 $${in}\:{A}\overset{\bigtriangleup} {{B}C}:\left({a},{b},{c},\:{as}\:{sides}\right) \\ $$$${D}:\:{midpoint}\:{of}\:{AC}, \\ $$$${BE}:\:{bisect}\:{of}\:\measuredangle{B},{and}\measuredangle{DBD}'. \\ $$$$\boldsymbol{{wanted}}: \\…
Question Number 177978 by mr W last updated on 11/Oct/22 Answered by mr W last updated on 11/Oct/22 $$\boldsymbol{{method}}\:\mathrm{1} \\ $$$${AB}={AF}={DC}=\mathrm{1} \\ $$$${BD}=\mathrm{2}\:\mathrm{sin}\:\mathrm{40}° \\ $$$$\frac{\mathrm{sin}\:\left({C}+\mathrm{110}°\right)}{\mathrm{sin}\:{C}}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{40}°}…
Question Number 46889 by ajfour last updated on 02/Nov/18 Commented by ajfour last updated on 02/Nov/18 $${Q}.\mathrm{46611}\:\left({Alternate}\:{approach}\right) \\ $$ Answered by ajfour last updated on…
Question Number 46864 by ajfour last updated on 01/Nov/18 Commented by ajfour last updated on 02/Nov/18 $${If}\:{a}\:{sphere}\:{of}\:{radius}\:\boldsymbol{{R}}\:{touches} \\ $$$${the}\:{walls}\:{at}\:{A},\:{B},\:{C}\:;\:{find}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}} \\ $$$${in}\:{terms}\:{of}\:\alpha,\beta,\gamma\:{and}\:{R}. \\ $$ Commented by…
Question Number 177910 by HeferH last updated on 11/Oct/22 Answered by mr W last updated on 11/Oct/22 Commented by mr W last updated on 11/Oct/22…
Question Number 46821 by Raj Singh last updated on 01/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Nov/18 $$\pi{RL}=\mathrm{1}.\mathrm{1}×{x} \\ $$$${L}=\sqrt{{R}^{\mathrm{2}} +{H}^{\mathrm{2}} }\: \\ $$$${H}=\mathrm{14}{m} \\…
Question Number 112318 by Aina Samuel Temidayo last updated on 07/Sep/20 $$\mathrm{A}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{has}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{properties}\:\mathrm{BC}=\mathrm{1},\:\boldsymbol{\mathrm{AB}}=\boldsymbol{\mathrm{AC}}\:\mathrm{and}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{angle}\:\mathrm{bisector}\:\mathrm{from}\:\mathrm{vertex}\:\mathrm{B}\:\mathrm{is} \\ $$$$\mathrm{also}\:\mathrm{a}\:\mathrm{median}.\:\mathrm{Find}\:\mathrm{all}\:\mathrm{possible} \\ $$$$\mathrm{triangle}\left(\mathrm{s}\right)\:\mathrm{with}\:\mathrm{its}/\mathrm{their} \\ $$$$\mathrm{side}−\mathrm{lengths}\:\mathrm{and}\:\mathrm{angles}. \\ $$ Commented…
Question Number 177832 by HeferH last updated on 09/Oct/22 Answered by mr W last updated on 10/Oct/22 Commented by mr W last updated on 10/Oct/22…
Question Number 112266 by Aina Samuel Temidayo last updated on 07/Sep/20 $$\mathrm{Let}\:\Omega\:\mathrm{denote}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\mathrm{ABC}. \\ $$$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\Omega\:\mathrm{at}\:\mathrm{A}\:\mathrm{meets}\:\mathrm{BC}\:\mathrm{at}\:\mathrm{X}. \\ $$$$\mathrm{Let}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{bisectors}\:\mathrm{of}\:\angle\mathrm{AXB}\:\mathrm{meet} \\ $$$$\mathrm{AC}\:\mathrm{and}\:\mathrm{AB}\:\mathrm{at}\:\mathrm{E}\:\mathrm{and}\:\mathrm{F} \\ $$$$\mathrm{respectively}.\:\mathrm{D}\:\mathrm{is}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{bisector}\:\mathrm{from}\:\angle\mathrm{BAC}\:\mathrm{on}\:\mathrm{BC}.\:\mathrm{Let}\:\mathrm{AD} \\ $$$$\mathrm{intersect}\:\mathrm{EF}\:\mathrm{at}\:\mathrm{K}\:\mathrm{and}\:\Omega\:\mathrm{again}\:\mathrm{at} \\…
Question Number 177796 by mr W last updated on 09/Oct/22 Commented by mr W last updated on 09/Oct/22 $${find}\:{the}\:{area}\:{of}\:{the}\:{square}. \\ $$ Commented by mr W…