Equal chords of a circle are equidistant from center

We can clearly see the blue graph, it is that of a circle which passes through point B and has its center at point A. CD is a chord of this circle. We can change the position of the four points (A, B, C and D). Size and position of the circle depends upon the positions of A and B. Length of the chord is dependent upon the position of the points C and D. We will see that when we move the points C and D the points G, H, E and F automatically change and lengths of GH and EF are always equal to the length of CD. We can also see the perpendiculars which have been drawn from the center of the circle on to the three chords (CD, GH and EF in green color).