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::xI::::::::::::::bMnCJA;W\\Hlysy:::::::::::::::::::::::vPt>W:RlvYxI:::::::::::::::::::::::i?nCjysy:ZqryvY::::::::::::::::: ::tBbMnGxIyA:vPJa:yay=::::::::::::::::::::::::::t@W\\H;:::::JqryvY:::: :::::::::::::::::::::::::::::::::::::::::::::::::::tBbMnGjy;:::::::::: :::::::W>nCt@ry::vPJa:yay=:::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::<:ry::::::::::::::ZZ@NbM:Zymy;:::::::::::::::::::::::i? nCjysy:ZqryvY:::::::::::::::::::XGi_ql^;yA:vPt>W:::::b]vYxI::::::::::::::::::::::::::::::::::::::::: ::::::::::::::roZql^;yA:::::::::::::::::vTjUSlZy=:jUcMnCjysy:::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::Z::xI:::::::::::::::W \\H;JqryvY:::::::::::::::::::::::jU;W:1:" }{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 260 16 "Travail dirig\351 9" }}{PARA 19 "" 0 "" {TEXT -1 39 "\251 Apprendre Maple. Al ain Le Stang. 2006" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 87 "Soit ABC un triangle du plan affine euclidien , M \+ un point quelconque que l'on projette" }}{PARA 0 "" 0 "" {TEXT -1 67 " orthogonalement en H1,H2,H3 sur (BC) , (CA) , (AB) respectivement ." } }{PARA 0 "" 0 "" {TEXT -1 83 "Montrer que M est sur le cercle circonsc rit \340 ABC si et seulement si H1,H2,H3 sont " }}{PARA 0 "" 0 "" {TEXT -1 31 "align\351s, sur la droite dite de " }{TEXT 256 6 "Simson " }{TEXT -1 14 " associ\351e \340 M:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 76 "On travaillera dans un rep\350re orthon ormal tel que A(0,0) , B(1,0) , C(-2,3)." }}}{PAGEBK }{PARA 259 "" 0 " " {TEXT -1 28 "Corrig\351 du Travail dirig\351 9:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart:with (geometry):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 257 26 "Traduction des hypoth\350ses:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "point(A,[0,0]):point(B,[1,0]):point(C,[-2,3]):po int(M,[X,Y]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "line(AB,[A ,B]):line(CA,[C,A]):line(BC,[B,C]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "projection(H1,M,BC):projection(H2,M,CA):projection(H3 ,M,AB):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "circle(cercle_ci rc,[A,B,C]):" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 258 41 "Appartenance de M au cercle circonscrit :" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 39 "equation1:=Equation(cercle_circ,[X,Y]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*equation1G/,**$)%\"XG\"\"#\"\"\"F+* $)%\"YGF*F+F+F)!\"\"*&\"\"&F+F.F+F/\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 259 35 "Condition d'alignement de \+ H1,H2,H3:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,Jor danBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcolG%'addrowG%$adjG%(a djointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%'bezoutG%,blockmatr ixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%)colspaceG%(colspan G%*companionG%'concatG%%condG%)copyintoG%*crossprodG%%curlG%)definiteG %(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotprodG%*eigenvalsG%,eig envaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG%&equalG%,exponenti alG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG%*frobeniusG%*gauss elimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)hadamardG%(hermiteG%(h essianG%(hilbertG%+htransposeG%)ihermiteG%*indexfuncG%*innerprodG%)int basisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jacobianG%'jordanG%'ke rnelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'matrixG%&minorG%(mi npolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normalizeG%*nullspaceG%'or thogG%*permanentG%&pivotG%*potentialG%+randmatrixG%+randvectorG%%rankG %(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scalarmulG%-sin gularvalsG%&smithG%,stackmatrixG%*submatrixG%*subvectorG%)sumbasisG%(s wapcolG%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*transposeG%,vandermo ndeG%*vecpotentG%(vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 165 "U1:=[HorizontalCoord(H1)-HorizontalCoord(H2), VerticalCoord(H1)-VerticalCoord(H2)]:\nU2:=[HorizontalCoord(H1)-Horizo ntalCoord(H3),VerticalCoord(H1)-VerticalCoord(H3)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "det(matrix([U1,U2]));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,*%\"YG#\"#:\"#E*&#\"\"$F'\"\"\"%\"XGF+F+*&#F*F'F+*$) F$\"\"#F+F+!\"\"*&#F*F'F+*$)F,F1F+F+F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "equation2:=-26/3*%=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*equation2G/,**$)%\"XG\"\"#\"\"\"F+*$)%\"YGF*F+F+F)!\"\"*&\"\" &F+F.F+F/\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "D'o\371 le r\351sultat , les \351quations 1 et 2 \+ \351tant \351quivalentes ." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "2 0" 39 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }