Question

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.

Answer 1

Let AB and CD be the two chords of the circle. The centre of the circle be O through which the diameter PQ passes.
Let the diameter PQ bisect the two chords and point R and S.
We know that the when the line passing through the centre of the circle bisects the chord then the line is perpendicular to the chord.
Thus, $\angle \mathrm{ARS}=\angle \mathrm{DSR}=90°$
AB will be thus parallel to CD and cut by the transversal PS as interior angle on the sam side of the transversal are equal.