Alternate name(s): perpendicular chord bisector theorem converse.
If a line (AB ) passing through the center of a circle cuts a chord (CD ) which does not pass through the center at right angles, then the line bisects the chord.
Original statement
ἐὰν ἐν κύκλῳ ϵὐθϵῖά τις διὰ τοῦ κέντρου ϵὐθϵῖάν τινα μὴ διὰ τοῦ κέντρου δίχα τέμνῃ, καὶ πρὸς ὀρθὰς αὐτὴν τέμνϵι: καὶ ἐὰν πρὸς ὀρθὰς αὐτὴν τέμνῃ, καὶ δίχα αὐτὴν τέμνϵι.
English translation
If in a circle a straight line through the centre bisects a straight line not through the centre, it also cuts it at right angles; and if it cuts it at right angles, it also bisects it.
