Figure Cabri II Plus vers. MS-Windows (MAC 1.40) Used macro polaire, no name Icon: 16x16 0 0 40 0 0 7 7 7 7 7 7 0 0 0 0 0 0 0 40 7 7 0 0 0 0 0 0 7 7 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 7 0 0 0 7 40 0 0 0 0 0 0 0 0 0 0 0 7 0 0 7 40 0 0 0 0 0 0 0 0 0 0 0 15 0 7 0 40 0 0 0 0 0 0 0 0 0 0 0 15 0 7 0 40 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 40 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 40 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 40 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 40 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7 40 0 0 0 0 0 0 0 0 0 0 0 7 0 0 7 40 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 7 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 40 7 7 0 0 0 0 0 0 7 7 0 0 0 0 0 40 0 0 7 7 7 7 7 7 0 0 0 0 0 Help: "Se donner un cercle et un point." Mth: 0 CN:2, ON:3, FN:1, PO:2 CT: circle, CS 1, point, CS 0, Const: Inv, Mth:0, 0, CN:2, VN:1, Const: 3 2 Line, Mth:1, 0, CN:2, VN:2, Const: 4 3 Perp, Mth:0, 1, CN:2, VN:2, Const: 4 5, color:V, Figure description: Window center x: 4.61cm y: -0.07cm Window size x: 35.46cm y: 18.32cm Resolution: 28 ppc 1: Pt, Val: 0 0 invisible, 2: Axes, Const: 1, cart, Val: 1 0 0 1 invisible, 3: Pt, Val: -2.28947368421053 -0.105263157894737 "O" TP: -2.64285714285714, 0.428571428571429, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 O}{50,91,152,267,268} 4: Cir, Const: 3, Val: 6.14669471795035 5: Pt, Val: -0.736842105263158 7.55263157894737 "A" TP: -0.464285714285714, 7.64285714285714, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 A}{50,91,152,267,268} 6: Pt, Val: -11.3157894736842 -5.78947368421053 "B" TP: -11.7142857142857, -5.75, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 B}{50,91,152,267,268} 7: Pt, Val: 6.18421052631579 -4.23684210526316 "C" TP: 6.21428571428571, -4.32142857142857, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 C}{50,91,152,267,268} Ma: polaire, Const: 4 i: 0 5 i: 0 10: Ma R, F No1, color:V, invisible, COLOR 128 0 0, Ma: polaire, Const: 6 i: 0 4 i: 0 13: Ma R, F No1, color:V, invisible, COLOR 128 0 0, Ma: polaire, Const: 7 i: 0 4 i: 0 16: Ma R, F No1, color:V, invisible, COLOR 128 0 0, 18: Int, Const: 13, 16, int ind:0, "A'" TP: -1.39285714285714, -7.42857142857143, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 A'}{50,91,152,267,268} 20: Int, Const: 16, 10, int ind:0, "B'" TP: 3.96428571428571, 4.14285714285714, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 B'}{50,91,152,267,268} 22: Int, Const: 10, 13, int ind:0, "C'" TP: -11.25, 6.75, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 C'}{50,91,152,267,268} 23: Line, Const: 5, 18, color:Bl, invisible, COLOR 255 0 0, 24: Line, Const: 6, 20, color:Bl, invisible, COLOR 255 0 0, 25: Line, Const: 22, 7, color:Bl, invisible, COLOR 255 0 0, 27: Int, Const: 23, 10, int ind:0, "A""" TP: -1.71428571428571, 5.17857142857143, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 A"}{50,91,152,267,268} 29: Int, Const: 13, 24, int ind:0, "B""" TP: -4.96428571428571, -2.07142857142857, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 B"}{50,91,152,267,268} 31: Int, Const: 25, 16, int ind:0, "C""" TP: 0.821428571428571, -1.42857142857143, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 7 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red245\green41\blue22;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 C"}{50,91,152,267,268} 32: Line, Const: 29, 31, color:Bl, invisible, COLOR 255 0 0, 33: Line, Const: 31, 27, color:Bl, invisible, COLOR 255 0 0, 34: Line, Const: 27, 29, color:Bl, invisible, COLOR 255 0 0, 36: Int, Const: 10, 4, int ind:0, color:Bl, COLOR 255 0 0, 37: Int, Const: 10, 4, int ind:0x10000, color:Bl, COLOR 255 0 0, 39: Int, Const: 13, 4, int ind:0, color:Bl, COLOR 255 0 0, 40: Int, Const: 13, 4, int ind:0x10000, color:Bl, COLOR 255 0 0, 42: Int, Const: 16, 4, int ind:0, color:Bl, COLOR 255 0 0, 43: Int, Const: 16, 4, int ind:0x10000, color:Bl, COLOR 255 0 0, 44: Seg, Const: 5, 37, color:Bl, COLOR 255 0 0, 45: Seg, Const: 5, 36, color:Bl, COLOR 255 0 0, 46: Seg, Const: 39, 6, color:Bl, COLOR 255 0 0, 47: Seg, Const: 6, 40, color:Bl, COLOR 255 0 0, 48: Seg, Const: 43, 7, color:Bl, COLOR 255 0 0, 49: Seg, Const: 7, 42, color:Bl, COLOR 255 0 0, 51: Int, Const: 32, 4, int ind:0, color:Bl, COLOR 255 0 0, "a2" TP: -8.75, -1.75, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 a2}{50,91,151,266,267} 52: Int, Const: 32, 4, int ind:0x10000, color:Bl, COLOR 255 0 0, "a1" TP: 3.92857142857143, -0.428571428571429, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 a1}{50,91,151,266,267} 54: Int, Const: 33, 4, int ind:0, color:Bl, COLOR 255 0 0, "b2" TP: 2.32142857142857, -4.17857142857143, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 b2}{50,91,151,266,267} 55: Int, Const: 33, 4, int ind:0x10000, color:Bl, COLOR 255 0 0, "b1" TP: -2.07142857142857, 6.64285714285714, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 b1}{50,91,151,266,267} 57: Int, Const: 34, 4, int ind:0, color:Bl, COLOR 255 0 0, "c2" TP: -0.0357142857142857, 6.14285714285714, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 c2}{50,91,151,266,267} 58: Int, Const: 34, 4, int ind:0x10000, "c1" TP: -6.85714285714286, -4.60714285714286, TS: 1.07142857142857, 0.821428571428571 p: 0, Arial, S: 12 C: 15 Fa: 0{\rtf1\mac\ansicpg10000\cocoartf824\cocoasubrtf440\'0a{\fonttbl\f0\fswiss\fcharset77 ArialMT;}\'0a{\colortbl;\red255\green255\blue255;\red0\green67\blue250;}\'0a\pard\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\ql\qnatural\pardirnatural\'0a\'0a\f0\fs24 \cf2 \dn2 c1}{50,91,151,266,267} 59: Seg, Const: 55, 5, color:R, COLOR 0 0 255, 60: Seg, Const: 55, 58, color:R, COLOR 0 0 255, 61: Seg, Const: 58, 6, color:R, COLOR 0 0 255, 62: Seg, Const: 58, 52, color:R, COLOR 0 0 255, 63: Seg, Const: 52, 7, color:R, COLOR 0 0 255, 64: Seg, Const: 52, 55, color:R, COLOR 0 0 255, 65: Seg, Const: 5, 57, color:ma, COLOR 255 0 255, 66: Seg, Const: 57, 54, color:ma, COLOR 255 0 255, 67: Seg, Const: 57, 51, color:ma, COLOR 255 0 255, 68: Seg, Const: 51, 6, color:ma, COLOR 255 0 255, 69: Seg, Const: 51, 54, color:ma, COLOR 255 0 255, 70: Seg, Const: 54, 7, color:ma, COLOR 255 0 255, 71: Seg, Const: 22, 27, color:Bl, COLOR 255 0 0, 72: Seg, Const: 27, 20, color:Bl, COLOR 255 0 0, 73: Seg, Const: 20, 31, color:Bl, COLOR 255 0 0, 74: Seg, Const: 31, 18, color:Bl, COLOR 255 0 0, 75: Seg, Const: 18, 29, color:Bl, COLOR 255 0 0, 76: Seg, Const: 29, 22, color:Bl, COLOR 255 0 0, 77: Seg, Const: 5, 27, color:Bl, COLOR 255 0 0, 78: Seg, Const: 27, 18, color:Bl, COLOR 255 0 0, 79: Seg, Const: 20, 29, color:Bl, COLOR 255 0 0, 80: Seg, Const: 29, 6, color:Bl, COLOR 255 0 0, 81: Seg, Const: 22, 31, color:Bl, COLOR 255 0 0, 82: Seg, Const: 31, 7, color:Bl, COLOR 255 0 0, 83: Seg, Const: 55, 27, color:Bl, COLOR 255 0 0, 84: Seg, Const: 27, 31, color:Bl, COLOR 255 0 0, 85: Seg, Const: 31, 54, color:Bl, COLOR 255 0 0, 86: Seg, Const: 57, 27, color:Bl, COLOR 255 0 0, 87: Seg, Const: 27, 29, color:Bl, COLOR 255 0 0, 88: Seg, Const: 29, 58, color:Bl, COLOR 255 0 0, 89: Seg, Const: 51, 29, color:Bl, COLOR 255 0 0, 90: Seg, Const: 29, 31, color:Bl, COLOR 255 0 0, 91: Seg, Const: 31, 52, color:Bl, COLOR 255 0 0, 92: Text, Val: 194 -213 0, nA, nP, "Les polaires de A, B, C par rapport au cercle forment un triangle A'B'C' homologique au triangle ABC. Plus prZcisZment: polaire(A)=B'C'; polaire(B)=C'A'; polaire(C)=A'B'. Soit A"" l'intersection de AA' et B'C'. Soit B"" l'intersection de BB' et C'A'. Soit C"" l'intersection de CC' et A'B'. Soient a1 et a2 les intersections de B""C"" et du cercle. Soient b1 et b2 les intersections de C""A"" et du cercle. Soient c1 et c2 les intersections de A""B"" et du cercle. a1b1c1 et a2b2c2 sont les triangles solutions du probl_me de Castillon. Ils sont inscrits dans le cercle et les cĒtZs bc, ca, ab passent respectivement par A,B,C. Il est utile de crZer une macro de la polaire d'un point M. Si M' est l'inverse de M par rapport au cercle, alors la polaire de M est la perpendiculaire en M' par rapport ö la droite OMM'. La figure est faite pour des raisons esthZtiques quand les points A, B, C sont extZrieurs au cercle, les polaires respectives Ztant matZrialisZes par les points de contact des tangentes issues de A, B, C. On peut d'ailleurs montrer que dans ce cas il y a toujours 2 solutions distinctes. Mais cela n'est pas nZcessaire, les points A, B, C peuvent Zventuellement se trouver ö l'intZrieur du cercle. On peut rZaliser une applet o_ les points A, B, C sont libres et visualiser l'existence ou la nonexistence des triangles solutions en dZpla_ant les points A, B, C." TP: 6.92857142857143, 7.60714285714286, TS: 14.3571428571429, 14.9285714285714 p: 0, Arial, S: 12 C: 40 Fa: 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