2
Question
If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.
If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.
Open in App
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 o
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 o
Since alternate angles are equal, we have:AB|| CD
Suggest Corrections
148
Similar questions