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Category: Geometry

Question-188845

Question Number 188845 by ajfour last updated on 07/Mar/23 Answered by a.lgnaoui last updated on 07/Mar/23 $$\bigtriangleup{OAB}\:\:\:\left({recrangle}\:{en}\:{O}\right) \\ $$$${AB}={a}+\frac{{a}\sqrt{\mathrm{2}}}{\mathrm{2}}\:\:\:\:\Rightarrow{AH}=\frac{{a}}{\mathrm{2}}+\frac{{a}\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$$${OA}={OB}\:={R} \\ $$$$\mathrm{sin}\:\frac{\pi}{\mathrm{4}}=\frac{{AH}}{{R}}\Rightarrow{R}=\frac{\mathrm{2}{AH}}{\:\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{R}}=\mathrm{1}+\sqrt{\mathrm{2}}…

Question-188755

Question Number 188755 by normans last updated on 06/Mar/23 Commented by mr W last updated on 06/Mar/23 $${with}\:{given}\:{data}\:{the}\:{area}\:{of}\:\Delta{CFE} \\ $$$${is}\:{not}\:{uniquely}\:{defined}!\: \\ $$$${it}'{s}\:{dependent}\:{from}\:{the}\:{angle}\:\angle{A}. \\ $$ Commented…

Question-188463

Question Number 188463 by emilagazade last updated on 01/Mar/23 Answered by mr W last updated on 01/Mar/23 $$\frac{{AO}}{{CO}}=\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{sin}\:\mathrm{70}} \\ $$$$\frac{{BO}}{{AO}}=\frac{\mathrm{sin}\:\mathrm{40}}{\mathrm{sin}\:\alpha} \\ $$$$\frac{{CO}}{{BO}}=\frac{\mathrm{sin}\:\left(\mathrm{20}−\alpha\right)}{\mathrm{sin}\:\mathrm{20}} \\ $$$$\left({i}\right)×\left({ii}\right)×\left({iii}\right): \\…