@options @figure; gogeometry = texte( -13.8 , -4.3 ,"Antonio Gutierrez. www.gogeometry.com") { kaki , dec1 , car-3 }; click = texte( -13.8 , -3.8 ,"Click the left button to start/stop the animation") { rougefonce , dec2 , car-2 }; hyp = texte( -14.8 , 5 ,"HYPOTESIS") { rougefonce , dec2 , car-2 }; explore = texte( -14.8 , 1 ,"TO EXPLORE:") { rouge , dec2 , car-2 }; explore1 = texte( -14.5 , 0.5 ,"1. Click the red button to start/stop animation") { rougefonce , dec2 , car-2 }; explore2 = texte( -14.5 , 0 ,"2. Activate the Step-by-Step construction bar:") { rougefonce , dec2 , car-2 }; explore2a = texte( -14.5 , -0.5 ," Press P and click the left mouse on any free area") { rougefonce , dec2 , car-2 }; explore3 = texte( -14.5 , -1 ,"3. Manipulate: Drag A, C, D, O, O1, O2, O3, O4") { rougefonce , dec2 , car-2 }; explore4 = texte( -14.5 , -1.5 ," at any step ") { rougefonce , dec2 , car-2 }; O = point( 3.33 , -0.13 ) { rouge }; N = point( 2.93 , 2.47 ) { i }; N1 = point( 3.47 , 1.57 ) { i }; ceNN1 = cercle( N , N1 ) { i }; xx = reel( 315 , 0 , 360 , 1 ) { oscille , (7.67,-8) , i }; var yy = 180*cos(xx)+180 { 307.279220613579 }; B = pointsur( ceNN1 , yy ) { rouge , rond2 , (-0.56,-0.77) }; ciAB = cercle( O , B ) { rouge , 2 , plein10 }; A = pointsur( ciAB , 139.34 ) { rouge , rond3 , (-0.5,-0.86) }; C = pointsur( ciAB , 308.66 ) { rouge , rond3 }; D = pointsur( ciAB , -96.93 ) { rouge , rond3 }; hyp1 = texte( -14.5 , 4.5 ,"1. Draw concyclic points A,B,C,D") { stop , rougefonce , dec2 , car-2 }; medAB = mediatrice( A , B ) { i }; O1 = pointsur( medAB , 3.62 ) { sansnom }; centro1 = texte( O1 ,"Ģi(O,1)") { vert , (-0.77,-0.2) , dec2 , car-2 }; hyp2 = texte( -14.5 , 4 ,"2. Draw four circles through AB, BC, CD and AD") { rougefonce , dec2 , car-2 }; ciO1A = cercle( O1 , A ) { stop , vert , plein10 }; medBC = mediatrice( B , C ) { i }; O2 = pointsur( medBC , 3.36 ) { sansnom }; centro2 = texte( O2 ,"Ģi(O,2)") { vert , (0.25,-0.37) , dec2 , car-2 }; ciO2B = cercle( O2 , B ) { stop , vert , plein10 }; medCD = mediatrice( C , D ) { i }; O3 = pointsur( medCD , 2 ) { sansnom }; centro3 = texte( O3 ,"Ģi(O,3)") { vert , (-0.03,-0.27) , dec2 , car-2 }; ciO3C = cercle( O3 , C ) { stop , vert , plein10 }; medAD = mediatrice( A , D ) { i }; O4 = pointsur( medAD , -2 ) { sansnom }; centro4 = texte( O4 ,"Ģi(O,4)") { vert , (-1.13,-0.3) , dec2 , car-2 }; ciO4D = cercle( O4 , D ) { stop , vert , plein10 }; hyp3 = texte( -14.5 , 3.5 ,"3. Draw intersections A',B',C',D'") { rougefonce , dec2 , car-2 }; A' = intersection( ciO1A , ciO4D , A ) { stop , rond3 , (-1,-0.43) }; B' = intersection( ciO1A , ciO2B , B ) { stop , rond3 , (0.1,-0.8) }; C' = intersection( ciO2B , ciO3C , C ) { stop , rond3 , (0.13,0) }; D' = intersection( ciO3C , ciO4D , D ) { stop , rond3 , (-0.5,0.03) }; medA'B' = mediatrice( A' , B' ) { i }; medA'D' = mediatrice( A' , D' ) { i }; O' = intersection( medA'B' , medA'D' ) { (0,-0.53) }; conc = texte( -14.8 , 2.5 ,"CONCLUSION TO PROVE:") { rougefonce , dec2 , car-2 }; conc1 = texte( -14.5 , 2 ,"1. A',B',C',D' are concyclic") { rougefonce , dec2 , car-2 }; ciO'A' = cercle( O' , A' ) { stop , 2 , plein10 }; @config; boutons=animation;