The line joining the mid-points of two chords of a circle passes through its centre. Prove that the chords are parallel.
Given : AB and CD are the two chords of a circle with centre O. L and M are the midpoints 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 centre 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.
Solution The Line Joining the Mid-points of Two Chords of a Circle Passes Through Its Centre. Prove that the Chords Are Parallel. Concept: Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line.