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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.
Solution
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.
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