Question

The line joining the midpoints of two chords of a circle passes through its center.

Prove that the chords are parallel.

Answer 1

Given: AB and CD are the two chords of a circle with center O.

L and M are the mid-points 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 center 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.