The line joining the mid-points of two chords of a circle passes through its centre. Prove that the
chords are parallel.
Given : AB and CD are the two chords of a circle with centre O.
L and M are the midpoints of AB and CD and O lies in the line joining ML
To prove: AB ∥ CD
Proof: AB and CD are two chords of a circle with centre O.
Line LOM bisects them at L and M
Then, OL ⊥ AB
And, OM ⊥ CD
∴ ∠ALM = ∠LMD = 90°
But they are alternate angles
∴ AB ∥ CD.