The perpendicular from the centre of a circle to a chord bisects the chord

BD ₌ DC

AD ⟂ BC

AD is the perpendicular from the 
centre of the circle to the chord BC

radius

CIRCLE

CHORD

RADIUS

POINT AND CIRCLE

CHORD

BD=DC

PERPENDICULAR

     Author-N UMA DEVI-copyright-BYSA

Author-N UMA DEVI-copyright-ccBYSA

A = (1.3109589752644761, 0.27173349800557023)
radius_1 = 5 (slider from 1 to 10, step 1)
c = Circle(A, radius_1)
C = Point(c)
B = Point(c)
g = LineBisector(B, C)
BC = Segment(B, C)
D = Intersect(g, BC)
DC = Distance(D, C)
h = Segment(A, D)
α = Angle(A, D, B)
β = Angle(C, D, A)
distanceBC = Distance(B, C)
BD: DC
BC_1: Name[B] + (Name[C]) + " = " + distanceBC
TextDC: Name[D] + (Name[C]) + " = " + DC
text3: "" + BD + "₌" + DC + ""
distanceBD = Distance(B, D)
TextBD: Name[B] + (Name[D]) + " = " + distanceBD
distanceCD = Distance(C, D)
TextCD: Name[C] + (Name[D]) + " = " + distanceCD
AB = Segment(A, B)
AC = Segment(A, C)
f = true
i = true
d = true
b = true
a = true
e = true