Question

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

Answer 1

Given: AB and CD are two chords of a circle with centre O. Diameter POQ bisects them at points L and M.
To prove: AB || CD
Proof: AB and CD are two chords of a circle with centre O. Diameter POQ bisects them at L and M.

Then OL ⊥ AB
Also, OM ⊥ CD
∴ ∠ ALM = ∠ LMD = 90^o
Since alternate angles are equal, we have:
AB|| CD