Question Number 19321 by ajfour last updated on 09/Aug/17 $$\mathrm{Parallel}\:\mathrm{tangents}\:\mathrm{to}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{at}\:\mathrm{A} \\ $$$$\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{cut}\:\mathrm{in}\:\mathrm{the}\:\mathrm{points}\:\mathrm{C}\:\mathrm{and}\:\mathrm{D} \\ $$$$\mathrm{by}\:\mathrm{a}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{at}\:\mathrm{E}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{AD},\:\mathrm{BC}\:\mathrm{and}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{joining}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{points}\:\mathrm{of}\:\mathrm{AE} \\ $$$$\mathrm{and}\:\mathrm{BE}\:\mathrm{are}\:\mathrm{concurrent}. \\ $$ Commented by ajfour…
Question Number 150263 by dany last updated on 10/Aug/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by puissant last updated on 10/Aug/21 $$\mathrm{limite}? \\…
Question Number 84259 by M±th+et£s last updated on 10/Mar/20 Commented by M±th+et£s last updated on 10/Mar/20 $${find}\:\frac{{y}}{{x}} \\ $$$${and}\:{z} \\ $$ Answered by mr W…
Question Number 18499 by chux last updated on 22/Jul/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}\:\mathrm{pounds}\:\mathrm{of}\:\mathrm{a}\:\mathrm{vertical} \\ $$$$\mathrm{cylindrical}\:\mathrm{tank}\:\mathrm{that}\:\mathrm{is}\:\mathrm{6ft}\:\mathrm{in}\:\mathrm{dia} \\ $$$$\mathrm{meter}\:\mathrm{and}\:\mathrm{15ft}\:\mathrm{in}\:\mathrm{height}.\mathrm{if}\:\mathrm{it}\:\mathrm{weig} \\ $$$$\mathrm{hs}\:\mathrm{20lbs}\:\mathrm{per}\:\mathrm{ft}\:\mathrm{of}\:\mathrm{height}. \\ $$ Commented by chux last updated on 23/Jul/17…
Question Number 18111 by ajfour last updated on 15/Jul/17 Commented by ajfour last updated on 15/Jul/17 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{R}.\:\mathrm{A}\:\mathrm{chord} \\ $$$$\mathrm{AB}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{through}\:\mathrm{point}\:\mathrm{M}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{diameter}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\boldsymbol{\phi}\:\mathrm{to}\:\mathrm{it}; \\ $$$$\:\mathrm{BM}:\mathrm{AM}=\mathrm{p}:\mathrm{q}\:.\:\mathrm{Through}\:\mathrm{point}\:\mathrm{B}\:\mathrm{is} \\ $$$$\mathrm{dropped}\:\:\mathrm{a}\:\mathrm{perpendicular}\:\mathrm{BC}\:\mathrm{to}\:\mathrm{the}…
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Question Number 18004 by ajfour last updated on 13/Jul/17 Commented by ajfour last updated on 13/Jul/17 $$\mathrm{The}\:\mathrm{angular}\:\mathrm{bisector}\:\mathrm{of}\:\angle\mathrm{ABC} \\ $$$$\mathrm{intersects}\:\mathrm{side}\:\mathrm{AD}\:\mathrm{at}\:\mathrm{point}\:\mathrm{M},\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{dropped}\:\mathrm{from} \\ $$$$\mathrm{vertex}\:\mathrm{A}\:\mathrm{to}\:\mathrm{side}\:\mathrm{BC}\:\mathrm{cuts}\:\mathrm{BC}\:\mathrm{at} \\ $$$$\mathrm{point}\:\mathrm{N}\:\mathrm{so}\:\mathrm{that}\:\mathrm{BN}=\mathrm{NC}\:\mathrm{and}…
Question Number 17963 by ajfour last updated on 13/Jul/17 Commented by ajfour last updated on 13/Jul/17 $$\mathrm{AB}=\mathrm{2a}\:\:,\:\:\mathrm{CD}=\mathrm{2b} \\ $$$$\mathrm{Find}\:\boldsymbol{\mathrm{r}}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:\:\mathrm{a},\mathrm{b},\phi,\:\mathrm{and}\:\mathrm{R}. \\ $$$$\mathrm{Hence}\:\mathrm{find}\:\mathrm{AP}^{\mathrm{2}} +\mathrm{BP}^{\mathrm{2}} +\mathrm{CP}^{\mathrm{2}} +\mathrm{DP}^{\mathrm{2}} .…
Question Number 17869 by ajfour last updated on 11/Jul/17 Commented by ajfour last updated on 11/Jul/17 $$\mathrm{Q}.\mathrm{17852}\:\:\left(\mathrm{solution}\right) \\ $$ Answered by ajfour last updated on…
Question Number 83285 by jagoll last updated on 29/Feb/20 $$\mathrm{3}^{\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}−\mathrm{4}\right)} \:\leqslant\:\mathrm{7}^{\mathrm{x}+\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{solution} \\ $$ Commented by jagoll last updated on 29/Feb/20 $$\mathrm{7}^{\mathrm{log}_{\mathrm{7}} \:\left(\mathrm{3}^{\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}−\mathrm{4}\right)} \right)\:}…