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Category: Geometry

Question-184609

Question Number 184609 by cherokeesay last updated on 09/Jan/23 Answered by ajfour last updated on 09/Jan/23 $$\mathrm{cos}\:\left(\mathrm{2}\alpha−\mathrm{90}°\right)=\frac{\mathrm{2}}{{R}} \\ $$$$\Rightarrow\:\:\mathrm{sin}\:\mathrm{2}\alpha=\frac{\mathrm{2}}{{R}}={t} \\ $$$$\mathrm{tan}\:\alpha=\frac{{R}+\sqrt{{R}^{\mathrm{2}} −\mathrm{4}}}{\mathrm{2}}=\frac{\mathrm{1}+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{\mathrm{2}{t}} \\ $$$$\mathrm{sin}\:\mathrm{2}\alpha=\frac{\mathrm{2tan}\:\alpha}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}}…

Question-53530

Question Number 53530 by MJS last updated on 23/Jan/19 Commented by MJS last updated on 23/Jan/19 $$\mathrm{I}\:\mathrm{found}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{question}\:\mathrm{53168}\:\mathrm{by} \\ $$$$\mathrm{Sir}\:\mathrm{Aifour} \\ $$ Answered by MJS last…

Determiner-1-AB-BC-AC-en-fonction-de-r-2-CBA-BAC-et-BCA-

Question Number 184557 by a.lgnaoui last updated on 08/Jan/23 $${Determiner} \\ $$$$\mathrm{1}\bullet\mathrm{AB},\:\:\mathrm{BC}\:\:\mathrm{AC}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\boldsymbol{\mathrm{r}} \\ $$$$\mathrm{2}\bullet\:\:\measuredangle\mathrm{CBA}\:;\:\:\measuredangle\mathrm{BAC}\:;{et}\:\measuredangle\mathrm{BCA} \\ $$ Commented by a.lgnaoui last updated on 08/Jan/23 Answered by…

Question-53422

Question Number 53422 by ajfour last updated on 21/Jan/19 Commented by ajfour last updated on 21/Jan/19 $${Find}\:{maximum}\:{inradius}\:{and} \\ $$$${minimum}\:{circumradius}\:{in}\:{terms} \\ $$$${of}\:{a}\:{and}\:{b}\:{if}\:{AB}\:{of}\:\bigtriangleup{ABC}\:{is}\:{variable}. \\ $$ Commented by…