If the diameter of a circle bisects each of the two chords of the circle, then both the chords:

are parallel to each other

L =  mid-point of AB.

OL⊥AB [ Line joining the centre of a circle to the mid-point of a chord is perpendicular to the chord]

= ALO = 90∘

Similarly, ∠OMD = 90^∘

Therefore, ∠ALO=∠OMD

But, these are alternate interior angles.

So, AB∥CD.