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Question
If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.
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Solution
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
Since alternate angles are equal, we have:AB|| CD
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
Since alternate angles are equal, we have:AB|| CD
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