22.5 Angle
Author: Guru

Measure ∡BCX
Measure ∡BCY

Steps of the construction - 
1. Construct Segment AB length 8
2. Plot point C in the middle of AB
3. Construct arc of radius 3 and cut 

Steps of the construction (menu option in brackets)

1. Draw Segment AB, length 8 (segment with given length)
2. Plot point C on AB (point on object)
3. Cut arcs h and i from Point C on both sides of AB (Arc)
4. Mark intersection points H and I (Intersect)
5. Same radius, cut 2 arcs from H and I and intersect (Intersect)
5a. Intersect point N (Arcs)
6. Draw Segment NC (Segment)
7. Measure ∡BCN  (90∘) (Angle)
8. Same radius, cut 2 arcs S and T (Arcs)
9. Intersect point X (Intersect)
10.Draw Segment XC (Segment)
11. Measure ∡XCB  (45∘) (Angle)
12. Same radius, cut 2 arcs from J and L (Arcs) 
and they intersect at Y (Intersect)
13. Draw Segment CY  (Segment)
14  Measure ∡YCL  (22.5∘) (Angle)

A = (-8.695964011017034, -0.127150031921885)
B = (7.11809706458288, 0.11029833257661148)
AB = Segment(A, B)
C = Point(AB)
c = Circle(C, 5)
D = Point(c)
E = Point(c)
d = CircleArc(C, D, E)
F = Point(c)
G = Point(c)
e = CircleArc(C, F, G)
H = Intersect(e, AB, 1)
I_1 = Intersect(d, AB, 1)
f = Circle(H, 8)
g = Circle(I_1, 8)
J_1 = Point(g)
K = Point(g)
h = CircleArc(I_1, J_1, K)
L_1 = Point(f)
M = Point(f)
k = CircleArc(H, L_1, M)
N = Intersect(h, k, 1)
i = Segment(N, C)
α = Angle(I_1, C, N)
p = Circle(C, 4)
O = Point(p)
P = Point(p)
q = CircleArc(C, O, P)
Q = Point(p)
R = Point(p)
r = CircleArc(C, Q, R)
S = Intersect(q, i, 1)
T = Intersect(r, AB, 1)
s = Circle(T, 7)
t = Circle(S, 7)
U = Point(t)
V = Point(t)
c_1 = CircleArc(S, U, V)
W = Point(s)
Z = Point(s)
d_1 = CircleArc(T, W, Z)
X = Intersect(c_1, d_1, 1)
j = Segment(C, X)
β = Angle(B, C, X)
L = Point(AB)
e_1 = Circle(C, L)
B_1 = Point(e_1)
C_1 = Point(e_1)
f_1 = CircleArc(C, B_1, C_1)
J = Intersect(f_1, j, 1)
g_1 = Circle(L, 4)
h_1 = Circle(J, 4)
E_1 = Point(h_1)
F_1 = Point(h_1)
k_1 = CircleArc(J, E_1, F_1)
G_1 = Point(g_1)
H_1 = Point(g_1)
p_1 = CircleArc(L, G_1, H_1)
Y = Intersect(k_1, p_1, 1)
l = Segment(C, Y)
γ = Angle(B, C, Y)

Tool: SquareTool
Tool2[ <Number>, <Point> ]
Input: side, A
Output: poly1

B = Point(Circle[A, side])
a = Segment(A, B)
c = Circle(A, side)
b = OrthogonalLine(A, a)
C = Intersect(c, b, 2)
d = Circle(C, side)
e = OrthogonalLine(C, b)
D = Intersect(d, e, 1)
poly1, a_1, b_1, d_1, c_1 = Polygon(A, B, D, C)