Move the point F or G to show 
segment length becoming zero

See if you demonstrate the idea of a tangent
 from chord as well

Show chord

Show diameter

Show line EF

A = (-8.055771013125815, -0.12756647165030896)
c = Circle(A, 5)
B = Point(c)
C = Point(c)
a = Segment(B, C)
D = (11.017260351109801, 1.782868525424199)
d = Circle(D, 5)
distanceCB = Distance(C, B)
TextCB: Name[C] + (Name[B]) + " = " + distanceCB
F = Point(d)
E = (11.925499939882926, -13.218743992587054)
b = Line(E, F)
G = Intersect(d, b, 2)
distanceFG = Distance(F, G)
TextFG: Name[F] + (Name[G]) + " = " + distanceFG
f = Line(E, D)
H = Intersect(d, f, 2)
I = Intersect(d, f, 1)
g = Segment(H, I)
distanceIH = Distance(I, H)
TextIH: Name[I] + (Name[H]) + " = " + distanceIH
h = Segment(G, F)
e = false
i = false
j = false