Question

The line joining the midpoints of two chords of a circle passing through its centre. Prove the chords are parallel.

Answer 1

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.