The perpendicular from the centre bisects the chord
drag point c and b arount the circle and visualise the effects of the theorm. notice the length from c to the line bisecting the chord and the lenght from b and the line bisecting the chord. are they the same lenght?
we will call the point that bisects the chord V.
proof: check
given the line ED and the chord CB, where ED is perpendicular to CB intersecting at point V, we will prove the diameter chord theorm.
first we constructed the two radii AC and AB.
since all radii are congrunt, angle AVC and AVB are equal
now since diameter ED is perpendicular to CB intersecting at point V, we know that angle AVC and AVB are right angles.
now we know that triangle AVC and triangle AVB are right angled triangles.
we also know that AV is a common lenght
thus triangle AVC and AVB equal
thus CV = VB