Category: Geometry

Question Number 79798 by ajfour last updated on 28/Jan/20 Commented by ajfour last updated on 28/Jan/20 $${Find}\:{b}.\:{If}\:{not}\:{unique},\:{then} \\ $$$${relate}\:{b}\:{with}\:{r}. \\ $$ Commented by key of…

Question Number 145244 by gsk2684 last updated on 03/Jul/21 $$\mathrm{consider}\:\mathrm{the}\:\mathrm{circle}\: \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{2}, \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{4}\right),\:\mathrm{B}\left(\mathrm{1},−\mathrm{5}\right).\:\mathrm{if}\:\mathrm{P}\:\mathrm{is}\: \\ $$$$\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{PA}+\mathrm{PB}\:\mathrm{is}\:\mathrm{maximum}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{P},\mathrm{A},\mathrm{B}\:\mathrm{are}\:\mathrm{collinear}\: \\ $$$$\mathrm{points}. \\…

Question Number 14145 by RasheedSindhi last updated on 28/May/17 Commented by RasheedSindhi last updated on 28/May/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\alpha+\beta+\gamma+\delta+\xi=\mathrm{180}° \\ $$ Answered by ajfour last…

Question Number 79649 by john santu last updated on 27/Jan/20 $$\mathrm{given}\:\mathrm{a},\mathrm{ar},\mathrm{ar}^{\mathrm{2}} ,\mathrm{ar}^{\mathrm{3}} ,…\:\mathrm{is}\:\mathrm{a}\:\mathrm{GPwith}\: \\ $$$$\mathrm{n}\rightarrow\infty\:,\mathrm{r}\:<\:\mathrm{1} \\ $$$$\mathrm{if}\::\:\mathrm{a},\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{ar},\mathrm{x}_{\mathrm{3}} ,\:\mathrm{x}_{\mathrm{4}} ,\mathrm{x}_{\mathrm{5}} ,\mathrm{x}_{\mathrm{6}} ,\mathrm{ar}^{\mathrm{2}} , \\…

Question Number 79609 by mr W last updated on 26/Jan/20 Commented by mr W last updated on 26/Jan/20 $${if}\:{the}\:{large}\:{square}\:{has}\:{the}\:{side}\:{length} \\ $$$$\mathrm{10},\:{find}\:{the}\:{radius}\:{r}\:{of}\:{the}\:{smallest} \\ $$$${circle}. \\ $$…