Question Number 19279 by aylee last updated on 08/Aug/17 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left(\frac{\mathrm{2}{x}}{{cot}\frac{\mathrm{1}}{{x}}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 19238 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}.\:\mathrm{Two} \\ $$$$\mathrm{points}\:{E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC}\:\mathrm{and}\:{CD},\:\mathrm{respectively},\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{EB}}{{EC}}\:=\:{m},\:\mathrm{and}\:\frac{{FC}}{{FD}}\:=\:{n}.\:\mathrm{Lines}\:{AE}\:\mathrm{and}\:{BF} \\ $$$$\mathrm{intersect}\:\mathrm{at}\:{G}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{AG}}{{GE}}\:=\:\frac{\left({m}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{1}\right)}{{mn}}. \\ $$ Commented by ajfour…
Question Number 150308 by ajfour last updated on 11/Aug/21 Commented by ajfour last updated on 11/Aug/21 $$\:\:{Q}.\mathrm{149894}\:\left({revisit}\right) \\ $$ Answered by ajfour last updated on…
Question Number 150305 by Tawa11 last updated on 10/Aug/21 Commented by Tawa11 last updated on 10/Aug/21 $$\mathrm{Find}\:\:\:\:\frac{\mathrm{R}}{\mathrm{r}} \\ $$ Answered by nimnim last updated on…
Question Number 84718 by Power last updated on 15/Mar/20 Answered by mr W last updated on 15/Mar/20 $${AC}^{\mathrm{2}} ={PA}^{\mathrm{2}} +{PC}^{\mathrm{2}} −\mathrm{2}×{PA}×{PC}\:\mathrm{cos}\:\mathrm{120}° \\ $$$$\Rightarrow{AC}^{\mathrm{2}} ={PA}^{\mathrm{2}} +{PC}^{\mathrm{2}}…
Question Number 19150 by Tinkutara last updated on 06/Aug/17 $$\mathrm{A}\:\mathrm{semicircle}\:\mathrm{is}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{both}\:\mathrm{legs}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{right}\:\mathrm{triangle}\:\mathrm{and}\:\mathrm{has}\:\mathrm{its}\:\mathrm{centre}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{hypotenuse}.\:\mathrm{The}\:\mathrm{hypotenuse}\:\mathrm{is} \\ $$$$\mathrm{partitioned}\:\mathrm{into}\:\mathrm{4}\:\mathrm{segments},\:\mathrm{with}\:\mathrm{lengths} \\ $$$$\mathrm{3},\:\mathrm{12},\:\mathrm{12},\:\mathrm{and}\:{x},\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:'{x}'. \\ $$ Commented by Tinkutara…
Question Number 84689 by mr W last updated on 15/Mar/20 Commented by mr W last updated on 15/Mar/20 $${the}\:{parabola}\:{is}\:{rolled}\:{along}\:{the}\:{circle} \\ $$$${as}\:{shown}. \\ $$$${find}\:{the}\:{equation}\:{of}\:{the}\:{parabola}\:{when} \\ $$$${the}\:{touching}\:{point}\:{is}\:{at}\:{the}\:{position}\:\theta.…
Question Number 84682 by Power last updated on 15/Mar/20 Commented by Power last updated on 15/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{painted}\:\mathrm{area}\:? \\ $$ Commented by mr W last updated…
Question Number 84655 by ajfour last updated on 14/Mar/20 Commented by ajfour last updated on 14/Mar/20 $${If}\:{area}\:{of}\:\bigtriangleup{ABC}\:\:{is}\:{equal}\:{to} \\ $$$${max}\:{trapezium}\:{area}\:{BCED}\:, \\ $$$${find}\:{r}\:{in}\:{terms}\:{of}\:{ellipse}\: \\ $$$${parameters}\:{a}\:{and}\:{b}. \\ $$…
Question Number 19104 by Tinkutara last updated on 04/Aug/17 $$\mathrm{Let}\:\mathrm{ABC}\:\mathrm{be}\:\mathrm{an}\:\mathrm{acute}-\mathrm{angled}\:\mathrm{triangle} \\ $$$$\mathrm{with}\:\mathrm{AC}\:\neq\:\mathrm{BC}\:\mathrm{and}\:\mathrm{let}\:\mathrm{O}\:\mathrm{be}\:\mathrm{the} \\ $$$$\mathrm{circumcenter}\:\mathrm{and}\:\mathrm{F}\:\mathrm{be}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:\mathrm{C}.\:\mathrm{Further},\:\mathrm{let}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y} \\ $$$$\mathrm{be}\:\mathrm{the}\:\mathrm{feet}\:\mathrm{of}\:\mathrm{perpendiculars}\:\mathrm{dropped} \\ $$$$\mathrm{from}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{respectively}\:\mathrm{to}\:\left(\mathrm{the}\right. \\ $$$$\left.\mathrm{extension}\:\mathrm{of}\right)\:\mathrm{CO}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{FO}\:\mathrm{intersects} \\ $$$$\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\Delta\mathrm{FXY},\:\mathrm{second}\:\mathrm{time} \\…