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Category: Geometry

Question-177415

Question Number 177415 by HeferH last updated on 04/Oct/22 Answered by TheHoneyCat last updated on 04/Oct/22 $$\mathrm{This}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{on}\:\mathrm{the}\:\mathrm{green}\:\left(\mathrm{upper}\right)\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{notation} \\ $$$$“\neq''\:\mathrm{means}\:\mathrm{that}\:\mathrm{it}\:\mathrm{is}\:\mathrm{isocelus}\:\left(\mathrm{like}\:\mathrm{usualy}\:\mathrm{in}\right. \\ $$$$\left.\mathrm{geometry}\right)\:\mathrm{than}\:\mathrm{it}\:\mathrm{CANNOT}\:\mathrm{also}\:\mathrm{be}\:\mathrm{a}…

Question-46308

Question Number 46308 by ajfour last updated on 23/Oct/18 Commented by ajfour last updated on 23/Oct/18 $${O}\:{is}\:{the}\:{centre}\:{of}\:{circle},\:{C}\:{the} \\ $$$${centre}\:{of}\:{the}\:{unit}\:{square}.\: \\ $$$${If}\:\left({i}\right)\:\alpha=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{3}},\:\:\left({ii}\right)\:\alpha=\mathrm{60}°,\: \\ $$$${find}\:{radius}\:{R}. \\…

If-z-3-what-is-the-maximum-and-minimum-value-of-z-1-i-3-

Question Number 111850 by bemath last updated on 05/Sep/20 $${If}\:\mid{z}\mid\:=\:\mathrm{3}\:,\:{what}\:{is}\:{the}\:{maximum} \\ $$$${and}\:{minimum}\:{value}\:{of}\:\mid{z}−\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\mid\:? \\ $$ Answered by ajfour last updated on 05/Sep/20 $${max}\mid{z}−\mathrm{1}+{i}\sqrt{\mathrm{3}}\mid=\mathrm{5} \\ $$$${min}\mid{z}−\mathrm{1}+{i}\sqrt{\mathrm{3}}\mid=\mathrm{1} \\…

Question-177205

Question Number 177205 by HeferH last updated on 02/Oct/22 Answered by mr W last updated on 02/Oct/22 $$\angle{CAD}=\mathrm{180}−\mathrm{120}−\mathrm{3}{x}=\mathrm{60}−\mathrm{3}{x} \\ $$$$\angle{CDB}=\mathrm{180}−\mathrm{3}{x} \\ $$$${applying}\:{law}\:{of}\:{sines}: \\ $$$$\frac{\mathrm{sin}\:\left(\mathrm{60}−\mathrm{3}{x}\right)}{{CD}}=\frac{\mathrm{sin}\:\mathrm{120}}{{AD}}\:\:\:…\left({i}\right) \\…

Question-46073

Question Number 46073 by ajfour last updated on 20/Oct/18 Commented by ajfour last updated on 20/Oct/18 $${Determine}\:{coordinates}\:{of}\:{A}; \\ $$$$\:\:\:{b}\:>\:{c}\:.\:{P}\:{is}\:{contact}\:{point}\:{of}\:{side} \\ $$$${AB}\:{of}\:\bigtriangleup{ABC}\:{with}\:{upper}\:{rim}\:{of} \\ $$$${cylinder}\:\left({height}\:{H},\:{radius}\:{R}\right). \\ $$…