If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Explanation

Given : two chords AB and CD in a circle of centre O.G and H are the mid-points of AB and CD respectively. The line joining G and H passes through the point O.
To prove: `AB|\ |CD`
Proof : `angle AGO=90^@` (the line segment joining the mid-points of a chord to the centre, is perpendicular to the chord)
and `angle DHO=90^@`
But these are the alternate angles
`therefore AB|\ |CD`