Fig := proc(t) 
local xD, yD, D, C, Ii, Points, tex,sol; 
global A, B, b, Omega1, EL1, EL2; 
xD := Omega1[1] + aa*cos(t); 
yD := bb*sin(t); 
D := [xD, yD]; 
C := [xD + b, yD]; 
sol:=solve({EQ(A,D),EQ(C,B)},{x,y});
Ii:=[subs(sol,x),subs(sol,y)]:
Points := pointplot([A[], B[], C[], C[], D[], E[], Omega1[]], symbol = solidcircle, color = [red], symbolsize = 6); 
tex := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"], [E[], "E"], [Omega1[], "Ω1"]], align = ["above", "right"]); 
display([polygonplot([A, B, C, D], color = blue, filled = true, transparency = 0.9), Points, tex, EL1, EL2,plot([D,Ii]),plot([Ii,C])], axes = normal, scaling = constrained); end proc:
Fig((3*Pi)/4):
display([seq(Fig((2*Pi*i)/40), i = 1 .. 80)], insequence = true);
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
I am sorry; How to manage with such a message. Thank you very much.

restart;
with(plots):
_local(D):

EQ := proc(M, N) local eq; eq := (y - M[2])/(x - M[1]) = (N[2] - M[2])/(N[1] - M[1]); end proc;
     EQ := proc (M, N) local eq; eq := (y-M[2])/(x-M[1]) = 

        (N[2]-M[2])/(N[1]-M[1]) end proc

On considère un trapèze dans lequel une base est fixe l'autre base a une longueur constante et la somme des 2 autres côtés est constaante.
Trouver :
1-. le lieu des sommets mobiles.
A := [xA, 0]:
B := [xA + a, 0]:
D := [xD, yD]:
C := [xD + b, yD]:
EQ(B, C);
E := [xA + a - b, 0]:
Omega1 := (A + E)/2;
Application numérique :
Lieux des sommets C et D

xA := -5:
a := 13:#a>=b
b := 7:
c := -3:
xD := -6:
xC := xD + c:

A:
B:
C:
D:
Ll:=11:aa:= Ll/2: 
cc := (a - b)/2:
bb := sqrt(aa^2 - cc^2):
el1 := (x - Omega1[1])^2/aa^2 + y^2/bb^2 = 1:
sol := solve(subs(x = xD, (x - Omega1[1])^2/aa^2 + y^2/bb^2 = 1), y):
yD := sol[1]:
el2 := (x - Omega1[1] - b)^2/aa^2 + y^2/bb^2 = 1:
EL1 := implicitplot(el1, x = -9 .. 4, y = -6 .. 6, color = blue):
EL2 := implicitplot(el2, x = -9 .. 12, y = -6 .. 12, color = blue):
Trap := polygonplot([A, B, C, D], color = blue, filled = true, transparency = 0.9):
Points := pointplot([A[], B[], C[], C[], D[], E[], Omega1[]], symbol = solidcircle, color = [red], symbolsize = 6):
tex := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"], [E[], "E"], [Omega1[], "Ω1"]], align = ["above", "right"]):
display([Trap, EL1, EL2, tex, Points], axes = normal, scaling = constrained):
Fig := proc(xD) 
local yD, D, C,Points,tex; 
global A, B, b, Omega, xA, xB, EL1, EL2; 
solve(subs(x = xD, (x - Omega1[1])^2/aa^2 + y^2/bb^2 = 1), y); 
yD := %[1]; D:= [xD, yD]; C := [xD + b, yD];
Points := pointplot([A[], B[], C[], C[], D[], E[], Omega1[]], symbol = solidcircle, color = [red], symbolsize = 6): 
tex := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"], [E[], "E"], [Omega1[], "Ω1"]], align = ["above", "right"]):
display([polygonplot([A, B, C, D], color = blue, filled = true, transparency = 0.9), Points,tex,EL1, EL2], axes = normal, scaling = constrained); 
end proc:

Fig(2):Fig(-4):
Fig([seq(-6 + 3*i/10), i = 1.20], insequence = true);
Error, (in Engine:-Dispatch) badly formed input to solve: not fully algebraic
;I don't understand this error message. Thank you gfor your help.
 

How to improve this program ? Thank you.

restart;
Equation de la conique
eqcon := (45 - 27*cos(alpha))*x^2 - 54*sin(alpha)*x*y + (45 + 27*cos(alpha))*y^2 - 8;
Delta := (-54*sin(alpha))^2 - 4*(45 - 27*cos(alpha))*(45 + 27*cos(alpha));
expand(%);
simplify(%);
Discriminant : Δ<0 ce qui correxpond à une ellipse
Eq := simplify(expand(subs(x = cos(alpha/2)*X - sin(alpha/2)*Y, y = sin(alpha/2)*X + cos(alpha/2)*Y, eqcon)));
kx := coeff(Eq, X, 2);
ky := coeff(Eq, Y, 2);
k := -tcoeff(Eq);

EQ := X^2/(sqrt(1/kx^2)*k) + Y^2/(sqrt(1/ky^2)*k) = 1;
Calcul du grand et du petit axe 
a := 1/sqrt(coeff(lhs(EQ), X, 2));
b := 1/sqrt(coeff(lhs(EQ), Y, 2));
print(X^2/('a^2') + Y^2/('b^2') = 1);
 

L’éventail de la Geisha
restart:with(plots):with(geometry):
NULL;
_EnvHorizontalName := 'x':
_EnvVerticalName := 'y':

NULL;
EqBIS := proc(P, U, V) 
local a, eq1, M1, t, PU, PV, bissec1; 
description "P est le sommet de l'angle dont on chercche la bissectrice" ;
a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2); 
M1 := P + a*t; eq1 := op(eliminate({x = M1[1], y = M1[2]}, t)); 
RETURN(op(eq1[2])); end proc:

with(plottools);
with(plots);

r1 := 1/2;
r2 := r1/2;
R := r1*(21 - 12*sqrt(3));
                            21      (1/2)
                       R := -- - 6 3     
                            2            

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);
b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);

with(geometry);
eq := EqBIS(<sqrt(3)/2, 1/2>, <0, 0>, <0, 1/2>);
line(bis, eq);
                         (1/2)                  
                eq := 2 3      y - 2 x + 4 y - 2

                              bis

OpT := 2*sqrt(r1*R);
line(lv, x = OpT);
intersection(Omega, bis, lv);
coordinates(Omega);
evalf(%);
                                (1/2)    
                      OpT := 2 3      - 3

                               lv

                             Omega

                 [                / (1/2)    \]
                 [   (1/2)      2 \3      - 1/]
                 [2 3      - 3, --------------]
                 [                     (1/2)  ]
                 [                2 + 3       ]

                  [0.464101616, 0.3923048456]

retarrt;
with(plots);
with(plottools);
[cos((5*Pi)/6), sin((5*Pi)/6)];
                        [  1  (1/2)  1]
                        [- - 3     , -]
                        [  2         2]

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);
b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);
NULL;
A:=[cos(Pi/6), sin(Pi/6)];
B:=[cos(5*Pi/6), sin(5*Pi/6)];
Oo:=[0,0];
Op:=[0,1/2];
poly:=[A,B,Oo];
R := r1*(21 - 12*sqrt(3))
                            [1  (1/2)  1]
                       A := [- 3     , -]
                            [2         2]

                           [  1  (1/2)  1]
                      B := [- - 3     , -]
                           [  2         2]

                          Oo := [0, 0]

                                [   1]
                          Op := [0, -]
                                [   2]

                [[1  (1/2)  1]  [  1  (1/2)  1]        ]
        poly := [[- 3     , -], [- - 3     , -], [0, 0]]
                [[2         2]  [  2         2]        ]

                            21      (1/2)
                       R := -- - 6 3     
                            2            

Omega := [2*sqrt(3) - 3, 2*(sqrt(3) - 1)/(2 + sqrt(3))];
Omega1 := [3 - 2*sqrt(3), 2*(sqrt(3) - 1)/(2 + sqrt(3))];

                     [                / (1/2)    \]
                     [   (1/2)      2 \3      - 1/]
            Omega := [2 3      - 3, --------------]
                     [                     (1/2)  ]
                     [                2 + 3       ]

                     [                 / (1/2)    \]
                     [    (1/2)      2 \3      - 1/]
           Omega1 := [-2 3      + 3, --------------]
                     [                      (1/2)  ]
                     [                 2 + 3       ]

r3 := 3/16;
EF := sqrt(r3);

                                  3 
                            r3 := --
                                  16

                               1  (1/2)
                         EF := - 3     
                               4       

r := (150 - 72*sqrt(3))/193*1/2;
alpha := -5/3*r + 1/2*1/2;
p := sqrt(3)/3*1/2 - sqrt(3)/18*r;
                          75    36   (1/2)
                     r := --- - --- 3     
                          193   193       

                             307   60   (1/2)
                  alpha := - --- + --- 3     
                             772   193       

               1  (1/2)   1   (1/2) /75    36   (1/2)\
          p := - 3      - -- 3      |--- - --- 3     |
               6          18        \193   193       /

p2 := textplot([[A[], "A"], [B[], "B"], [Oo[], "O"]], align = ["above", "right"]);
display(a, b, p2, polygonplot(poly, thickness = 3, color = blue, transparency = 0.3), circle(Omega, R, color = blue, filled = true), circle(Omega1, R, color = blue, filled = true), circle([0, 3/4], 1/4, color = yellow, filled = true), circle([EF, 1/2 + r3], r3, color = green, filled = true), circle([-EF, 1/2 + r3], r3, color = green, thickness = 5), circle([p, 3/4 + alpha], r, color = red, thickness = 5), circle([-p, 3/4 + alpha], r, color = red, thickness = 5), axes = none, scaling = constrained, size = [500, 500]);
how to put color inside circles ? Thabk you.

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 11:
r := 7:
a := sqrt(R*r):

b := 2:
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [R + 2*b + r, 0]), r]):
ellipse(p, (x - R - b)^2/b^2 + y^2/a^2 = 1):
draw([C1(color = yellow, filled = true), 
C2(color = red, filled = true), p(color = blue, filled = true), 
C1(color = black), C2(color = black), p(color = black)], 
axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained):
alpha := arctan((R - r)/(R + 2*b + r));
long := cos(alpha)*(R + 2*b + r);
evalf(%);
circle(C2, [point(P2, [long, r - R]), r]);
rotation(p1, p, alpha, 'clockwise');
detail(p1);
point(A, 0, -R);
point(B, long, -R);
line(L1, [A, B]);
point(cen, [(143*sqrt(5))/25, -(26*sqrt(5))/25]);
reflection(L2, L1, cen);
detail(L2);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  L2

draw([C1(color = yellow, filled = true), C2(color = red, filled = true), p1(color = blue, filled = true), C1(color = black), C2(color = black), p1(color = black), L1(color = black)], axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained);
A Bug in reflection ? Why these error messages. Thank you.