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