Question Number 79004 by mr W last updated on 22/Jan/20 Commented by mr W last updated on 22/Jan/20 $${In}\:{a}\:{rectangle}\:{the}\:{radii}\:{r}_{{a}} ,{r}_{{b}} ,{r}_{{c}} \:{are} \\ $$$${given}.\:{Find}\:{the}\:{radius}\:{r}\:{of}\:{the} \\…
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Question Number 13434 by Nayon last updated on 20/May/17 $$\Delta{ABC}\sim\Delta{DEF}\: \\ $$$$\Delta{ABC}=\mathrm{25} \\ $$$$\Delta{DEF}=\mathrm{35} \\ $$$$\frac{\Sigma{Madian}^{\mathrm{2}} {of}\:\Delta{ABC}}{\Sigma{Madian}^{\mathrm{2}} \:{of}\:\Delta{DEF}}=? \\ $$ Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated…
Question Number 78937 by mr W last updated on 21/Jan/20 Commented by mr W last updated on 21/Jan/20 $${As}\:{shown},\:{the}\:{areas}\:{of}\:{three}\:{parts}\:{of} \\ $$$${a}\:{rectangle}\:{are}\:{given}.\:{Find}\:{the}\:{area} \\ $$$${of}\:{the}\:{fourth}\:{part}. \\ $$…
Question Number 78933 by TawaTawa last updated on 21/Jan/20 Commented by TawaTawa last updated on 21/Jan/20 $$\mathrm{Please}\:\mathrm{sirs},\:\mathrm{help}\:\mathrm{me}. \\ $$ Commented by TawaTawa last updated on…
Question Number 13305 by prakash jain last updated on 18/May/17 $$\mathrm{Does} \\ $$$$\mathrm{sin}\:\mathrm{A}=\mathrm{sin}\:\mathrm{B} \\ $$$$\mathrm{imply}\:\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}=\mathrm{sin}\frac{\mathrm{B}}{\mathrm{2}}? \\ $$$$\mathrm{For}\:\mathrm{example}\:\mathrm{A}=\pi\:\mathrm{and}\:\mathrm{B}=−\pi? \\ $$ Answered by ajfour last updated on…
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Question Number 13236 by Abbas-Nahi last updated on 17/May/17 $${For}\:{positive}\:\:{a},{b},{c}\:\:{such}\:{that}\:\:{a}\:{b}\:{c}=\mathrm{1} \\ $$$${show}\:{that}\:\:{a}^{{b}+{c}} \:\:{b}^{{c}+{a}} \:\:{c}^{{a}+{b}} \:\leqslant\mathrm{1} \\ $$$${solution}: \\ $$$${a}^{{b}+{c}} \:\:{b}^{{c}+{a}} \:\:{c}^{{a}+{b}} \:=\left({a}^{{b}} {a}^{{c}} \:{b}^{{c}} {b}^{{a}}…
Question Number 13228 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/May/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/May/17 $${in}\:{triangle}\:{ABC},{show}\:{that}: \\ $$$$\boldsymbol{{r}}=\sqrt{\boldsymbol{{r}}_{\boldsymbol{{a}}} .\boldsymbol{{r}}_{\boldsymbol{{b}}} }+\sqrt{\boldsymbol{{r}}_{\boldsymbol{{b}}} .\boldsymbol{{r}}_{\boldsymbol{{c}}} }+\sqrt{\boldsymbol{{r}}_{\boldsymbol{{c}}} .\boldsymbol{{r}}_{\boldsymbol{{a}}} }\:.…