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Question
The line joining the midpoints of two chords of a circle passes through its center.
Prove that the chords are parallel.
Solution
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.
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