input geometriesyr16; %---------------------------------------------------------------------------- % Exercice 4 numérique %---------------------------------------------------------------------------- figure (-8u,-8u,10u,8u); pair K,L,M; L=(0,0); M=(4u,0); K=(0,2u); draw K--L--M--cycle; trace codeperp(K,L,M,5); nomme.top(K); nomme.bot(L); nomme.bot(M); label.lft(btex $\sqrt{3}-1$ etex, 0.5[L,K]); label.bot(btex $\sqrt{3}+1$ etex, 0.5[L,M]); fin; %--------------------------------------------------------------------------- %---------------------------------------------------------------------------- % Exercice 2 géométrique %---------------------------------------------------------------------------- figure (-u,-u,12u,7u); pair A,B,C,D,E; D=(0,0); C=(8u,0); path dd; dd=cercles(D,4.5u); A=point(length dd *60/360) of dd; E=6/4.5[D,A]; B=A shifted(8u,0); draw A--B--C--D--cycle; trace demidroite(A,E); nomme.ulft(A); nomme.top(B); nomme.bot(C); nomme.bot(D); nomme.ulft(E); marque_p := "croix"; MarquePoint(E); fin; %---------------------------------------------------------------------------- % Exercice 1 géométrique %---------------------------------------------------------------------------- figure (0,0,12u,7u); pair A,B,C,O; trace grille(0.5) withcolor orange; B=(3u,4.5u); O=(4u,4.5u); A=(4u,5.5u); C=(9.5u,u); pickup pencircle scaled 1pt; draw (0.5u,6.5u)--(u,6.5u)--(u,6u)--(0.5u,6u)--(0.5u,5.5u)--(u,5.5u); draw (1.5u,6.5u)--(2u,6.5u)--(2u,5.5u)--(1.5u,5.5u)--cycle; draw (2.5u,6.5u)--(3u,6.5u)--(3u,5.5u)--(2.5u,5.5u)--cycle; draw (3.5u,6.5u)--(4u,6.5u)--(4u,5.5u)--(3.5u,5.5u)--cycle; marque_p := "plein"; MarquePoint(A); MarquePoint(B); MarquePoint(C); MarquePoint(O); label.lrt(btex $( \Delta )$ etex,(6u,7u)); draw (6u,0)--(6u,7u); nomme.urt(A); nomme.ulft(B); nomme.lrt(C); nomme.urt(O); fin; %---------------------------------------------------------------------------- % Exercice 3 géométrique %---------------------------------------------------------------------------- u:=0.75cm; figure (-8u,-8u,10u,8u); pair O,A,B,E,F,G,H; path aa,bb; path cc,arc; O=(0,0); aa=cercles(O,0.8u); bb=cercles(O,9u); A=point(length aa *15/360) of aa; B=point(length bb *15/360) of bb; E=point(length aa *345/360) of aa; F=point(length bb *345/360) of bb; aa:= subpath(length aa*270/360,length aa* 450/360) of aa; bb:= subpath(length bb*270/360,length bb* 450/360) of bb; cc := buildcycle(E--F,bb,B--A,aa); trace hachurage(cc,60,0.2,0); draw cc; G=symetrie(A,O); H=symetrie(E,O); draw A--E--G--H--cycle; draw G--A; draw H--E; nomme.top(O); nomme.ulft(A); nomme.top(B); nomme.llft(E); nomme.bot(F); fin; %---------------------------------------------------------------------------- % Problème (1) %---------------------------------------------------------------------------- u:=0.75cm; figure (-10u,-20u,10u,8u); pair A,B,C,D,O,S,T; A=(0,0); B=(6u,0); C=(8u,u); D=(2u,u); O=0.5[A,C]; T= O shifted (0,-6u); S=O shifted (0,-9u); draw A--B--C--D--cycle; draw A--C; draw B--D; draw A--S--B; draw S--C; draw S--D dashed evenly; draw O--S dashed evenly; draw T--A dashed evenly; draw T--B dashed evenly; draw T--C dashed evenly; draw T--D dashed evenly; draw (0,-8u)--(8u,-8u)--(6u,-10u)--(-2u,-10u)--cycle; draw (-2u,-10u)--(-2u,-11u)--(6u,-11u)--(6u,-10u); draw (6u,-11u)--(8u,-9u)--(8u,-8u); nomme.lft(A); nomme.top(B); nomme.top(C); nomme.top(D); nomme.top(O); nomme.llft(T); nomme.lrt(S); fin; %---------------------------------------------------------------------------- % Problème (2) %---------------------------------------------------------------------------- u:=1cm; figure (0,0,11u,13u); trace grille(0.1) withcolor orange; drawarrow (0,u)--(11u,u); drawarrow (u,0)--(u,13u); label.bot(btex $1$ etex,(2u,u)); label.llft(btex $0$ etex,(u,u)); label.lft(btex $10$ etex,(u,2u)); label.llft(btex $x$ etex,(11u,u)); label.rt(btex Volume de pierre de la fontaine etex,(u,12.5u)); fin; %--------------------------------------------------------------------------- end