Category: Geometry

Question Number 191205 by ajfour last updated on 20/Apr/23 Commented by ajfour last updated on 20/Apr/23 $${Find}\:\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{r}_{{i}} \:\:.\:{Take}\:{r}_{\mathrm{1}} ={a},\:\theta=\alpha \\ $$ Commented by…

Question Number 60085 by mr W last updated on 17/May/19 Commented by mr W last updated on 17/May/19 $${the}\:{edge}\:{length}\:{of}\:{cube}\:{is}\:{a}. \\ $$$${find}\:{the}\:{minimum}\:{distance}\:{between} \\ $$$${the}\:{blue}\:{lines}. \\ $$…

Question Number 191060 by Mingma last updated on 17/Apr/23 Answered by witcher3 last updated on 18/Apr/23 $$\mathrm{BS}=\mathrm{a}\frac{\mathrm{d}}{\mathrm{b}},\mathrm{BR}=\frac{\mathrm{d}}{\mathrm{b}}\mathrm{c} \\ $$$$\mathrm{AP}=\mathrm{c}\frac{\mathrm{d}}{\mathrm{a}},\mathrm{AQ}=\mathrm{b}\frac{\mathrm{d}}{\mathrm{a}} \\ $$$$\mathrm{CM}=\mathrm{a}.\frac{\mathrm{d}}{\mathrm{c}},\mathrm{NC}=\frac{\mathrm{d}}{\mathrm{c}}\mathrm{b} \\ $$$$\mathrm{c}\left(\mathrm{1}−\frac{\mathrm{d}}{\mathrm{a}}\right)=\mathrm{BP},\mathrm{c}\left(\mathrm{1}−\frac{\mathrm{d}}{\mathrm{b}}\right)=\mathrm{RA} \\ $$$$\mathrm{PR}=\mathrm{c}\left(\frac{\mathrm{d}}{\mathrm{a}}+\frac{\mathrm{d}}{\mathrm{b}}−\mathrm{1}\right)…

Question Number 125508 by ajfour last updated on 11/Dec/20 Commented by ajfour last updated on 11/Dec/20 $${Find}\:{R}. \\ $$ Answered by ajfour last updated on…

Question Number 125384 by ajfour last updated on 10/Dec/20 Commented by ajfour last updated on 10/Dec/20 $${The}\:{hemisphere}\:{has}\:{radius}\:\mathrm{2}. \\ $$$${The}\:{outer}\:{circular}\:{base}\:{has}\:{radius} \\ $$$$\mathrm{3}.\:{Find}\:{maximum}\:{side}\:{length}\:{of} \\ $$$${equilateral}\:{triangle}\:{with}\:{vertices} \\ $$$${placed}\:{as}\:{shown}.…