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Category: Geometry

Question-33452

Question Number 33452 by ajfour last updated on 16/Apr/18 Commented by ajfour last updated on 16/Apr/18 $${Find}\:{length}\:{of}\:{shadow}\:{s}\:{of}\:{a}\: \\ $$$${stick}\:{of}\:{length}\:\boldsymbol{{l}}\:{when}\:{source} \\ $$$${of}\:{light}\:{is}\:{a}\:{point}\:{source}\:{at} \\ $$$${height}\:{H}\:{above}\:{ground}. \\ $$…

Question-98675

Question Number 98675 by Algoritm last updated on 15/Jun/20 Commented by Algoritm last updated on 16/Jun/20 $$\mathrm{someone}\:\mathrm{gave}\:\mathrm{me}\:\mathrm{an}\:\mathrm{original}\:\mathrm{picture}\:\mathrm{and}\:\mathrm{I}'\mathrm{ll}\:\mathrm{translate}\:\mathrm{it} \\ $$ Commented by mr W last updated…

Question-164178

Question Number 164178 by mr W last updated on 15/Jan/22 Commented by mr W last updated on 15/Jan/22 $${two}\:{points}\:{P},\:{Q}\:{lie}\:{on}\:{the}\:{parabola} \\ $$$${with}\:{PQ}={b}.\:{find}\:{the}\:{locus}\:{of}\:{its} \\ $$$${midpoint}\:{M}.\:{find}\:{the}\:{lowest}\:{possible} \\ $$$${position}\:{of}\:{M}.…

Question-164174

Question Number 164174 by mr W last updated on 15/Jan/22 Commented by mr W last updated on 15/Jan/22 $${find}\:{the}\:{position}\:{of}\:{point}\:{P}\:{in}\:{a} \\ $$$${given}\:{triangle}\:{such}\:{that}\:{the}\:{sum} \\ $$$${of}\:{its}\:{distances}\:{to}\:{the}\:{vertices}\:{is} \\ $$$${minimum}.\:{find}\:{the}\:{corresponding}…

Question-163921

Question Number 163921 by ajfour last updated on 11/Jan/22 Answered by mr W last updated on 12/Jan/22 $${R}={radius}\:{of}\:{big}\:{circles} \\ $$$${r}={radius}\:{of}\:{small}\:{circles} \\ $$$${semi}\:{diagonal}={R}+\sqrt{\mathrm{2}}{R}=\sqrt{\left({R}+{r}\right)^{\mathrm{2}} −{R}^{\mathrm{2}} }+\sqrt{\mathrm{2}}{r} \\…