Question

Proove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other

Answer 1

Answer:

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Step-by-step explanation:

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