Question

Two chords AB and CD of a circle are parallel and a line L is the perpendicular bisector of AB. Show that L bisects CD.

Answer 1

We know that the perpendicular bisector of any chord of a circle always passes through the centre of the circle.

Since, L is the perpendicular bisector of AB.
Therefore, L passes through the centre of the circle.
But L ⊥ AB and AB || CD 
⇒ L ⊥ CD 
Thus, L ⊥ CD and passes through the centre of the circle.
So, L is perpendicular bisector of CD.