BC=8cm

D

A

B_1

B_2

B_3

C'

A'

A'BC' is the required triangle

Draw aline through C' parellel to AC which intersect extended BA at A'.

Draw a line through B_3 parellel to B_2C, intersecting the extended line segment BC at C'

Join B_2C

Locate three points B_1, B_2 and B_3 on BX so that bB_1 = B_1B_2 = B_2B_3

Draw a ray BX making an acute angle with  BC on the side opposite to the vertex A

Join AB and AC, ABC is the given triangle

Identify a point A 4cm away from D on the perpendicular bisector

Construct a perpendicular bisector of BC which intersect BC at D

Draw a line segment BC of 8cm

Construct an isosceles triangle whose base is 8cm and altitude 4cm and then another triangle whose sides are 3/2 times the corresponding sides of the triangle

Tick the box to get the steps

Author - Sathi K
$\copyright$ CC by SA

B = (1.58, -0.66)
C = Point(Circle[B, 8])
f = Segment(B, C)
c = Circle(B, 4.5)
d = Circle(C, 4.5)
A = Intersect(c, d, 1)
D = Intersect(c, d, 2)
g = OrthogonalLine(A, f)
E = Point(g)
F = Point(g)
h = Segment(E, F)
G = Point(c)
H = Point(c)
I = Point(c)
J = Point(c)
K = Point(d)
L = Point(d)
M = Point(d)
N = Point(d)
e = CircleArc(B, H, G)
k = CircleArc(B, J, I)
p = CircleArc(C, K, L)
q = CircleArc(C, M, N)
O = Intersect(f, h)
r = Circle(O, 4)
P = Intersect(r, h, 1)
Q = Point(r)
R = Point(r)
s = CircleArc(O, R, Q)
i = Segment(P, B)
j = Segment(P, C)
X = (10.72, -7.64)
l = Ray(B, X)
α = Angle(X, B, C)
t = Circle(B, 3)
S = Intersect(t, l, 1)
c_1 = Circle(S, 3)
T = Intersect(c_1, l, 2)
d_1 = Circle(T, 3)
U = Intersect(d_1, l, 2)
V = Point(t)
W = Point(t)
Z = Point(c_1)
A_1 = Point(c_1)
B_1 = Point(d_1)
C_1 = Point(d_1)
e_1 = CircleArc(B, W, V)
f_1 = CircleArc(S, A_1, Z)
g_1 = CircleArc(T, C_1, B_1)
m = Segment(T, C)
n = Line(U, m)
a = Line(B, C)
D_1 = Intersect(n, a)
b = Segment(C, D_1)
h_1 = Circle(T, 2)
E_1 = Intersect(h_1, l, 1)
F_1 = Intersect(h_1, m, 1)
k_1 = CircleArc(T, F_1, E_1)
p_1 = Circle(U, 2)
G_1 = Intersect(p_1, l, 1)
H_1 = Intersect(p_1, n, 2)
q_1 = CircleArc(U, H_1, G_1)
i_1 = Segment(E_1, F_1)
r_1 = Circle(E_1, 3.02)
I_1 = Point(r_1)
J_1 = Point(r_1)
s_1 = CircleArc(E_1, J_1, I_1)
t_1 = Circle(G_1, 3.02)
K_1 = Point(t_1)
L_1 = Point(t_1)
c_2 = CircleArc(G_1, L_1, K_1)
j_1 = Segment(U, D_1)
l_1 = Line(D_1, j)
m_1 = Line(B, P)
d_2 = Circle(C, 2)
M_1 = Intersect(d_2, f, 1)
N_1 = Point(d_2)
O_1 = Intersect(d_2, j, 1)
e_2 = CircleArc(C, N_1, M_1)
f_2 = Circle(D_1, 2)
P_1 = Intersect(f_2, b, 1)
Q_1 = Intersect(f_2, l_1, 1)
R_1 = Point(f_2)
g_2 = CircleArc(D_1, R_1, P_1)
h_2 = Circle(M_1, 1.53)
k_2 = Circle(P_1, 1.53)
S_1 = Intersect(e_2, h_2, 1)
T_1 = Intersect(j, l_1)
U_1 = Intersect(g_2, k_2)
V_1 = Point(h_2)
W_1 = Point(h_2)
Z_1 = Point(k_2)
A_2 = Point(k_2)
p_2 = CircleArc(P_1, A_2, Z_1)
q_2 = CircleArc(M_1, W_1, V_1)
B_2 = Intersect(l_1, m_1)
n_1 = Segment(D_1, B_2)
a_1 = Segment(P, B_2)
o = true
u = true
v = true
w = true
b_1 = true
o_1 = true
u_1 = true
v_1 = true
w_1 = true
a_2 = true
b_2 = true