Eighth Circle Theorem: 'Perpendicular bisects the chord'

Eighth circle theorem: 'Perpendicular bisects the chord' [this is a test version - I want to put a number of Circle Theorem ggb pages here, & am finding out how it all works!!] You are here: Home > Maths intro > Circle theorems first page > Perpendicular & chord Perpendicular & chord Perpendicular from the centre ,A, cutting a chord of the circle. CD is the chord, and AE is perpendicular to it. Move C or D, and note the connection between lengths CE and DE. If you want to alter the size of the circle, move A or B.
As CE is always the same as DE,you can see that 'the perpendicular from the centre to a chord bisects the chord'. If you need them, the theorems are summarised here [link needs to go here] Tim Devereux, Created with GeoGebra