Question

Straight line passing through centre $O$ of circle bisects chord $AB$ and $CD$ prove that the chords are parallel.

Answer 1

Given: $AB$ and $CD$ be two chords of a circle whose centre is $O$.

Let $PQ$ be a diameter (Straight line passing through centre $O$ of circle) bisecting chords $AB$ and $CD$ at $L$ and $M$ respectively.

Now,

$L$ is mid-point of $AB$.

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

$\angle ALO={90}^o$

Similarly, $\angle CMO={90}^o$

Therefore, $\angle ALO=\angle CMO$

But, these are corresponding angles.

So, $AB\parallel CD$.