Question

The line joining the mid-points of two chords
of a circle passes through its centre. Prove
that the chords are parallel.

Answer 1

Answer:

Given : E and F are mid points of 2 chords AB and CD respectively.

Line EF passes through centre.

To prove : AB||CD

∠OFC = ∠OEA = 90° as line drawn through the centre to bisect the chord is ⟂ to chord considering EF as traversal for lines AB and CD as alternate interior angles on same side are equal.

Therefore, AB || CD