Question

prove that, if a diameter of a circle them those chords are parallel to each other ​

Answer 1

Let AB and CD be two chords of a circle whose centre is O, and let PQ be a diameter bisecting chords AB and CD at L and M respectively.

Since PQ is a diameter. So, it passes through the centre O of the circle.

Now, L is 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, ∠CMO=90°

Therefore, ∠ALO = ∠CMO

But, these are corresponding angles.

So, AB||CD.