Question Number 181581 by HeferH last updated on 27/Nov/22 Answered by a.lgnaoui last updated on 27/Nov/22 $$\bigtriangleup\mathrm{ACD}\:\:\:\measuredangle\mathrm{ADC}=\mathrm{162}\:\:\:\mathrm{sin}\:\left(\mathrm{162}\right)=\mathrm{sin}\:\mathrm{18} \\ $$$$\frac{\mathrm{AC}}{\mathrm{sin}\:\mathrm{18}}=\frac{\mathrm{CD}}{\mathrm{sin}\:\mathrm{12}}\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\measuredangle\mathrm{BDC}=\mathrm{18}\:\:\measuredangle\mathrm{DCB}=\mathrm{162}−\alpha \\ $$$$\frac{\mathrm{BD}}{\mathrm{sin}\:\left(\mathrm{162}−\alpha\right)}=\frac{\mathrm{CD}}{\mathrm{sin}\:\alpha}\:\left(\mathrm{BD}=\mathrm{AC}\right)\Rightarrow \\ $$$$\frac{\mathrm{AC}}{\mathrm{sin}\:\left(\mathrm{162}−\alpha\right)}=\frac{\mathrm{CD}}{\mathrm{sin}\:\alpha}\:\:\left(\mathrm{2}\right)…
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Question Number 50460 by ajfour last updated on 16/Dec/18 Commented by ajfour last updated on 16/Dec/18 $${Find}\:\boldsymbol{{r}}\:{in}\:{terms}\:{of}\:\boldsymbol{{R}}. \\ $$ Commented by MJS last updated on…
Question Number 181496 by Acem last updated on 26/Nov/22 Answered by mr W last updated on 26/Nov/22 $${rectangle}\:{A}=\mathrm{2}{xh} \\ $$$${x}^{\mathrm{2}} +\left({x}+{h}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xh}+{h}^{\mathrm{2}}…
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Question Number 181485 by mr W last updated on 25/Nov/22 $${two}\:{medians}\:{of}\:{a}\:{triange}\:{are}\:\mathrm{3}\:{and} \\ $$$$\mathrm{4}\:{cm}\:{respectively}.\:{find}\:{the}\:{maximum} \\ $$$${area}\:{of}\:{the}\:{triangle}. \\ $$ Answered by Acem last updated on 26/Nov/22 Commented…
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Question Number 181437 by mnjuly1970 last updated on 25/Nov/22 Answered by MJS_new last updated on 25/Nov/22 $$\mathrm{let}\:{d},\:\sqrt{{b}^{\mathrm{2}} +{d}^{\mathrm{2}} }\:\mathrm{the}\:\mathrm{other}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangular} \\ $$$$\mathrm{triangle} \\ $$$${p}+{q}=\sqrt{{b}^{\mathrm{2}} +{d}^{\mathrm{2}} };\:{h}^{\mathrm{2}}…
Question Number 181432 by mr W last updated on 25/Nov/22 Commented by mr W last updated on 25/Nov/22 $${find}\:{the}\:{area}\:{of}\:{circle}. \\ $$ Commented by universe last…
Question Number 50352 by mr W last updated on 16/Dec/18 $${The}\:{distances}\:{from}\:{a}\:{point}\:{to}\:{the}\:{sides} \\ $$$${of}\:{a}\:{triangle}\:{are}\:{p},{q},{r}.\:{Find}\:{the}\: \\ $$$${maximum}\:\left({or}\:{minimum}\right)\:{area}\:{of}\:{the} \\ $$$${triangle},\:{if}\:{it}\:{exists}. \\ $$$${Assume}\:{r}\leqslant{q}\leqslant{p}. \\ $$ Commented by ajfour last…