Question

M and N are the midpoints of chords AB and CD . The line MN passes through the centre O . Prove that AB || CD.

Answer 1

AM = MB

CN = ND

∴ OM ⊥ AB

and ON ⊥ CD
(A line bisecting the chord and passing through the centre of the circle is perpendicular to the chord)

∴ ∠ OMA = ∠ OND = 90° each

But these are alternate interior angles

∴ AB || CD