Step 1

Step 2

Step 3

Dupliquer PQRS

P_1Q_1R_1S_1 semblable
circonscrit au carré PRR'P'

Caractérisation de la similitude
P_1Q_1R_1S_1 → PQRS
(Q_1→Q et S_1→S)

Step 4

Application de la similitude
PRR'P' → ABCD

P = (-3.403278688524586, 0.8747528624437946)
Q = (-2.1786, 3.824952862443795)
R = (1, 1)
S = (-1.282622950819668, -1.87344385886768)
pq = Line(P, Q)
qr = Line(Q, R)
rs = Line(R, S)
ps = Line(P, S)
PQ = Segment(P, Q)
QR = Segment(Q, R)
RS = Segment(R, S)
PS = Segment(S, P)
R' = Rotate(P, 90°, R)
P' = Rotate(R, (-(90°)), P)
u = Vector(P, P')
Q' = Translate(Q, u)
S' = Translate(S, u)
PR = Segment(P, R)
PP' = Segment(P, P')
P'R' = Segment(P', R')
RR' = Segment(R', R)
P'Q' = Segment(Q', P')
Q'R' = Segment(Q', R')
P'S' = Segment(P', S')
R'S' = Segment(S', R')
ck = Circle(Q, P, R)
qs = Line(Q, S)
I = Mirror(Q, OrthogonalLine[Center[ck], qs])
ck' = Circle(P', R', S')
qs' = Line(Q', S')
J = Mirror(S', OrthogonalLine[Center[ck'], qs'])
ij = Line(J, I)
Q_1 = Mirror(I, OrthogonalLine[Center[ck], ij])
S_1 = Mirror(J, OrthogonalLine[Center[ck'], ij])
ps_1 = Line(S_1, P')
pq_1 = Line(P, Q_1)
P_1 = Intersect(ps_1, pq_1)
rs_1 = Line(R', S_1)
qr_1 = Line(Q_1, R)
R_1 = Intersect(rs_1, qr_1)
PQ_1 = Segment(P_1, Q_1)
QR_1 = Segment(Q_1, R_1)
RS_1 = Segment(R_1, S_1)
PS_1 = Segment(S_1, P_1)
ck_1 = Circle(I, S, S_1)
Ω = Mirror(I, Line[Center[ck], Center[ck_1]])
r = Segment(Ω, Q)
r_1 = Segment(Ω, Q_1)
k: r / r_1
α = Angle(Q_1, Ω, Q)
A = Dilate(Rotate[P, α, Ω], k, Ω)
B = Dilate(Rotate[R, α, Ω], k, Ω)
C = Dilate(Rotate[R', α, Ω], k, Ω)
D = Dilate(Rotate[P', α, Ω], k, Ω)
AB = Segment(A, B)
BC = Segment(B, C)
CD = Segment(C, D)
AD = Segment(D, A)
ABCD, a_{1}, b_{1}, c_{2}, d_1 = Polygon(A, B, C, D)
a = false
b = false
c = false
d = false
r_P = Segment(P, Ω)
r_A = Segment(Ω, A)
β = Angle(P, Ω, A)
QS = Segment(S, Q)
g = Segment(Q', S')
Q_1S_1 = Segment(Q_1, S_1)