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.[br][br]proof: check[br][br]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.[br]first we constructed the two radii AC and AB.[br]since all radii are congrunt, angle AVC and AVB are equal[br][br]now since diameter ED is perpendicular to CB intersecting at point V, we know that angle AVC and AVB are right angles. [br]now we know that triangle AVC and triangle AVB are right angled triangles.[br]we also know that AV is a common lenght[br]thus triangle AVC and AVB equal[br]thus CV = VB[br][br][br][br][br][br]