Question Number 148993 by gsk2684 last updated on 02/Aug/21 $${if}\:{M}\:{is}\:{a}\:{point}\:{on}\:{the}\:{line}\:{y}={x}\:{and} \\ $$$${points}\:{P}\left(\mathrm{0},\mathrm{1}\right),{Q}\left(\mathrm{2},\mathrm{0}\right)\:{are}\:{such}\:{that} \\ $$$${PM}+{PQ}\:{is}\:{minimum}\:{then}\:{find}\:{P} \\ $$ Commented by mr W last updated on 02/Aug/21 $${i}\:{think}\:{the}\:{question}\:{should}\:{be}…
Question Number 83471 by mr W last updated on 02/Mar/20 Commented by mr W last updated on 02/Mar/20 $${The}\:{distances}\:{from}\:{a}\:{point}\:{M}\:{to}\:{the} \\ $$$${vertices}\:{of}\:{a}\:{given}\:{triangle}\:{with} \\ $$$${side}\:{lengthes}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:{are}\:\boldsymbol{{p}},\:\boldsymbol{{q}},\:\boldsymbol{{r}} \\ $$$${respectively}.…
Question Number 148991 by gsk2684 last updated on 02/Aug/21 $${The}\:{largest}\:{value}\:{of}\:{k}\:{for}\:{which}\: \\ $$$${the}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={k}^{\mathrm{2}} \:{lies}\:{completely} \\ $$$${in}\:{the}\:{interior}\:{of}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}+\mathrm{16}\:? \\ $$ Answered by mr…
Question Number 17901 by chux last updated on 12/Jul/17 Commented by chux last updated on 12/Jul/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{big}\:\mathrm{and} \\ $$$$\mathrm{small}\:\mathrm{circle} \\ $$ Commented by chux last…
Question Number 17886 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17 $$\left.\mathrm{1}\right){circle}\:{radius}={R} \\ $$$$\left.\mathrm{2}\right){acute}\:{angle}\:{between}\:{chords}:{AB}\:,\:{CD}=\varphi \\ $$$${find}:\:{AP}^{\mathrm{2}} +{BP}^{\mathrm{2}} +{CP}^{\mathrm{2}} +{DP}^{\mathrm{2}} .…
Question Number 17884 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 $${diagonals}\:{of}\:{trapezoid}:\:{ABCD},{create} \\ $$$$\mathrm{4}\:{triangles}.{area}\:{of}\:{two}\:{this}\:{triangles} \\ $$$${are}\:{equail}\:{to}:\:{a}^{\mathrm{2}} \:,{and}\:,\:{b}^{\mathrm{2}} . \\ $$$${find}\:{area}\:{of}\:{trapezoid}\:{in}\:{terms}\:{of}:\:{a},{b}.…
Question Number 83411 by ajfour last updated on 02/Mar/20 Commented by ajfour last updated on 02/Mar/20 $${Given}\:{a}\:{regular}\:{triangular} \\ $$$${pyramid}\:{with}\:{base}\:{sides}\:\boldsymbol{{a}}\:{and} \\ $$$${lateral}\:{edges}\:\boldsymbol{{a}}\sqrt{\mathrm{2}}.\:{A}\:{sphere} \\ $$$${passes}\:{through}\:{A}\:{and}\:{is}\:{tangent} \\ $$$${to}\:{the}\:{lateral}\:{edges}\:{SB}\:{and}\:{SC}…
Question Number 148932 by vvvv last updated on 01/Aug/21 $$\frac{\left(\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} }{\boldsymbol{{bc}}}\boldsymbol{{l}}_{\boldsymbol{{a}}} ^{\mathrm{2}} +\frac{\left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)^{\mathrm{2}} }{\boldsymbol{{ab}}}\boldsymbol{{l}}_{\boldsymbol{{c}}} ^{\mathrm{2}} +\frac{\left(\boldsymbol{{a}}+\boldsymbol{{c}}\right)^{\mathrm{2}} }{\boldsymbol{{ac}}}\boldsymbol{{l}}_{\boldsymbol{{b}}} ^{\mathrm{2}} =\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} \\ $$$$\boldsymbol{{l}}_{\boldsymbol{{b}}} ,\boldsymbol{{l}}_{\boldsymbol{{a}}} ,\boldsymbol{{l}}_{\boldsymbol{{c}}} −\boldsymbol{{bissekterissa}} \\…
Question Number 83369 by Power last updated on 01/Mar/20 Commented by mr W last updated on 01/Mar/20 $$\angle{A}=\mathrm{90}° \\ $$$$\Rightarrow{AD}={BD}={DC}=\mathrm{5} \\ $$ Commented by mathmax…
Question Number 83354 by TawaTawa1 last updated on 01/Mar/20 Commented by jagoll last updated on 01/Mar/20 $$\mathrm{NC}\:=\:\mathrm{MC}\:=\:\mathrm{x} \\ $$$$\mathrm{2x}^{\mathrm{2}} \:=\:\mathrm{25}\:\Rightarrow\mathrm{x}^{\mathrm{2}} \:=\:\frac{\mathrm{25}}{\mathrm{2}} \\ $$$$\mathrm{area}\:\mathrm{triangle}\:=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \:=\:\frac{\mathrm{25}}{\mathrm{4}}\: \\…