The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle

a = 3.5 (slider from 0 to 10)
A = (8.445283210853177, 7.887000101709866)
c = Circle(A, a)
B = Point(c)
α = 1.6231562043547265 rad (slider from 0 to 180°)
B' = Rotate(B, α, A)
β = Angle(B, A, B')
f = Segment(B, A)
g = Segment(A, B')
C = Point(c)
h = Segment(B, C)
i = Segment(C, B')
γ = Angle(B, C, B')
text1: "" + β + "⁼2₍" + γ + "₎"
InputBox1 = Textfield()
text2: "angle" + B + "" + A + "" + B' + " equal to 2 times angle" + B + "" + C + "" + B' + "
"
text3: "guru
ANGLE IS   " + β + " AND  " + γ + ""