Question Number 14365 by RasheedSindhi last updated on 31/May/17 $$\mathrm{Related}\:\mathrm{to}\:\mathrm{Q}#\mathrm{14157} \\ $$$$\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{ab}=\alpha^{\mathrm{2}} \\ $$$$\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{bc}=\beta^{\mathrm{2}} \\ $$$$\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} −\mathrm{cd}=\gamma^{\mathrm{2}} \\ $$$$\mathrm{d}^{\mathrm{2}} +\mathrm{e}^{\mathrm{2}}…
Question Number 145379 by ajfour last updated on 04/Jul/21 Commented by ajfour last updated on 04/Jul/21 $${The}\:{inner}\:{circles}\:{have}\:{unit}\:{radii}. \\ $$$${Find}\:{radius}\:{of}\:{outer}\:{circle}. \\ $$ Answered by mr W…
Question Number 145370 by imjagoll last updated on 04/Jul/21 $$\mathrm{There}\:\mathrm{are}\:\mathrm{two}\:\mathrm{circles}\:,\:\mathrm{C}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{1}\:\mathrm{and}\:\mathrm{C}_{\mathrm{r}} \: \\ $$$$\mathrm{of}\:\mathrm{radius}\:\mathrm{r}\:\mathrm{which}\:\mathrm{intersect}\:\mathrm{on}\:\mathrm{a}\:\mathrm{plain}\: \\ $$$$\mathrm{At}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{intersecting} \\ $$$$\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circumferences}\:\mathrm{of} \\ $$$$\mathrm{C}\:\mathrm{and}\:\mathrm{C}_{\mathrm{r}} \:,\mathrm{the}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{C}\:\mathrm{and} \\ $$$$\mathrm{that}\:\mathrm{to}\:\mathrm{C}_{\mathrm{r}} \:\mathrm{form}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{120}°\:\mathrm{outside} \\ $$$$\mathrm{of}\:\mathrm{C}\:\mathrm{and}\:\mathrm{C}_{\mathrm{r}}…
Question Number 79794 by mr W last updated on 28/Jan/20 Commented by mr W last updated on 28/Jan/20 $${Find}\:{the}\:{radii}\:{of}\:{two}\:{circles}\:\left({if}\:{exist}\right) \\ $$$${which}\:{touch}\:{each}\:{other}\:{and}\:{touch}\:{the} \\ $$$${parabola}\:{and}\:{the}\:{y}−{axis}\:{respectively}. \\ $$…
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 145246 by gsk2684 last updated on 03/Jul/21 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{inscribed}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{r}\:\mathrm{having}\:\mathrm{maximum} \\ $$$$\mathrm{area}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{with} \\ $$$$\mathrm{side}\:\sqrt{\mathrm{3}}\mathrm{r}. \\ $$ Answered by Olaf_Thorendsen last updated on 03/Jul/21…
Question Number 145244 by gsk2684 last updated on 03/Jul/21 $$\mathrm{consider}\:\mathrm{the}\:\mathrm{circle}\: \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{2}, \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{4}\right),\:\mathrm{B}\left(\mathrm{1},−\mathrm{5}\right).\:\mathrm{if}\:\mathrm{P}\:\mathrm{is}\: \\ $$$$\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{PA}+\mathrm{PB}\:\mathrm{is}\:\mathrm{maximum}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{P},\mathrm{A},\mathrm{B}\:\mathrm{are}\:\mathrm{collinear}\: \\ $$$$\mathrm{points}. \\…
Question Number 79694 by mr W last updated on 27/Jan/20 Commented by mr W last updated on 27/Jan/20 $${Three}\:{circles}\:{with}\:{radii}\:\alpha,\:\beta,\:\gamma\:{have} \\ $$$${their}\:{centres}\:{at}\:{the}\:{vertexes}\:{of}\:{a} \\ $$$${triangle}\:{with}\:{sides}\:{a},\:{b},\:{c}. \\ $$$${Find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{circle}\:{which}…
Question Number 14145 by RasheedSindhi last updated on 28/May/17 Commented by RasheedSindhi last updated on 28/May/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\alpha+\beta+\gamma+\delta+\xi=\mathrm{180}° \\ $$ Answered by ajfour last…
Question Number 79675 by ajfour last updated on 27/Jan/20 Commented by ajfour last updated on 27/Jan/20 $${The}\:{square}\:{has}\:{side}\:{s}. \\ $$$${Can}\:{we}\:{find}\:{a}\:{set}\:{of}\:{radii}\:{values}? \\ $$ Commented by ajfour last…