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Category: Geometry

In-a-AB-C-a-b-c-2-h-a-h-b-h-c-a-2-b-2-c-2-6abc-h-a-2-h-b-2-h-c-2-6h-a-h-b-h-c-find-A-

Question Number 75849 by behi83417@gmail.com last updated on 18/Dec/19 $$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{A}}\overset{\bigtriangleup} {\boldsymbol{\mathrm{B}C}}: \\ $$$$\begin{cases}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=\mathrm{2}\left(\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} \right)}\\{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{abc}}}\\{\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{2}} +\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} =\mathrm{6}\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}}…

solve-simultaneously-m-4-n-4-9m-2-n-2-1-i-m-n-4-ii-

Question Number 10222 by Tawakalitu ayo mi last updated on 30/Jan/17 $$\mathrm{solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{m}^{\mathrm{4}} \:+\:\mathrm{n}^{\mathrm{4}} \:=\:\mathrm{9m}^{\mathrm{2}} \mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1}\:\:\:\:\:\:\:……\:\left(\mathrm{i}\right) \\ $$$$\mathrm{m}\:+\:\mathrm{n}\:=\:\mathrm{4}\:……..\:\left(\mathrm{ii}\right) \\ $$ Commented by prakash…

Question-141291

Question Number 141291 by mr W last updated on 17/May/21 Commented by mr W last updated on 17/May/21 $${OB}=\sqrt{\left({R}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} }=\sqrt{{R}^{\mathrm{2}} −\mathrm{2}{Rr}} \\ $$$${AB}={R}+\sqrt{{R}^{\mathrm{2}} −\mathrm{2}{Rr}}=\frac{{r}}{\mathrm{tan}\:\mathrm{22}.\mathrm{5}°}…

The-number-of-integral-solutions-of-the-equation-7-y-1-y-2-y-2-1-y-2-9-are-

Question Number 10195 by priyank last updated on 30/Jan/17 $${The}\:{number}\:{of}\:{integral}\:{solutions}\:{of}\:{the}\:{equation}\: \\ $$$$\mathrm{7}\left({y}+\frac{\mathrm{1}}{{y}}\right)−\mathrm{2}\left({y}^{\mathrm{2}} +\frac{\mathrm{1}}{{y}^{\mathrm{2}} }\right)=\mathrm{9}\:\mathrm{are}? \\ $$ Commented by prakash jain last updated on 30/Jan/17 $${y}+\frac{\mathrm{1}}{{y}}={u}…

Let-A-be-a-subset-of-0-1-1997-containing-more-than-1000-elements-Prove-that-A-contains-either-a-power-of-2-or-two-distinct-integers-whose-sum-is-a-power-of-2-

Question Number 10181 by 0942679167 last updated on 29/Jan/17 $${Let}\:{A}\:{be}\:{a}\:{subset}\:{of}\:\left\{\mathrm{0};\mathrm{1};\centerdot\centerdot\centerdot;\mathrm{1997}\right\}\: \\ $$$${containing}\:{more}\:{than}\:\mathrm{1000}\:{elements}. \\ $$$${Prove}\:{that}\:{A}\:{contains}\:{either}\:{a}\:{power} \\ $$$${of}\:\mathrm{2}\:{or}\:{two}\:{distinct}\:{integers}\:{whose}\: \\ $$$${sum}\:{is}\:{a}\:{power}\:{of}\:\mathrm{2}. \\ $$ Terms of Service Privacy Policy…

Question-10166

Question Number 10166 by Joel575 last updated on 28/Jan/17 Commented by Joel575 last updated on 28/Jan/17 $$\mathrm{Two}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{same}\:\mathrm{center}\:\mathrm{point}\:\mathrm{have} \\ $$$$\mathrm{R}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{R}_{\mathrm{2}} \:\mathrm{with}\:\mathrm{R}_{\mathrm{1}} \:<\:\mathrm{R}_{\mathrm{2}} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{long}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{bowstring}\:\mathrm{is}\:\mathrm{10}\:\mathrm{cm}, \\…