To show that Equal chords of a circle are equidistant from the centre

∴ CD = GF

Distance from the centre

AI = AH

Note: Move the Slider to change the radius of the circle.
Move the external points to change the angle at the centre.

a = 7.6 (slider from 1 to 9, step 0.1)
A = (-6.973066193181729, 0.034340536263509185)
c = Circle(A, a)
B = Point(Circle[A, 15])
b = Segment(A, B)
d, e = Tangent(B, c)
C = Intersect(c, d, 1)
D = Intersect(c, e, 1)
E = Point(Circle[A, 15])
f = Segment(A, E)
g, h = Tangent(E, c)
F = Intersect(c, g, 1)
G = Intersect(c, h, 1)
β_1 = Angle(E, A, B)
i = Segment(C, D)
j = Segment(G, F)
H = Intersect(b, i)
I = Intersect(f, j)
k = Segment(A, H)
l = Segment(A, I)
text2: "Chord CD = " + i + ""
text3: "Chord GF = " + j + ""
text6: "AI = " + l + ""
text7: "AH = " + k + ""