Question

2 chords PQ and RS of a circle are parallel and AB is the perpendicular bisector of PQ without using any construction prove that AB bisects RS

Answer 1

Answer:

Theorem

If a diameter is perpendicular to a chord, then the diameter bisects the chord.

Step-by-step explanation:

It is given that,

2 chords PQ and RS of a circle are parallel and

AB is the perpendicular bisector of PQ.

From this we get AB is the diameter of the circle .

Since PQ || RS,  AB is also perpendicular to RS.

And AB is a diameter.

Therefore AB bisects RS.

Answer 2

Answer:

Theorem

If a diameter is perpendicular to a chord then the diameter bisects the chord

Step-by-step explanation:

2 chords PQ and RS of a circle are parallel and

AB is perpendicular bisector of PQ

Therefore AB is also perpendicular to RS

and AB is thus the diameter

Therefore AB bisects RS