Activity 1
Drag D around and verify if ∠D maintains any relationship with ∠C or ∠O

Activity 2
Drag F to other side of the arc BA. How are angles related to angle at the centre theorem  ? 

O = (5.66, -1.12)
H = (0.96, -3.1)
c = Circle(O, H)
A = Point(c)
B = Point(c)
C = Point(c)
f = Segment(B, C)
g = Segment(C, A)
h = Segment(B, O)
i = Segment(O, A)
α = Angle(A, O, B)
β = Angle(A, C, B)
D = (5.12, 0.34)
j = Segment(A, D)
k = Segment(D, B)
γ = Angle(A, D, B)
F = Point(c)
n = Segment(A, F)
p = Segment(F, B)
ε = Angle(A, F, B)