Mathematics
AB and CD are two parallel chords of a circle and a line l is the perpendicular bisector of AB. Show that l is the perpendicular bisector of CD also.
Circles
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Answer
We know that,
The perpendicular bisector of a chord passes through the centre of the circle.
∴ l bisects AB, l ⟂ AB
Given, AB ∥ CD
If a line is perpendicular to one of two parallel lines, it is also perpendicular to the other.
Now, l ⟂ AB and AB ∥ CD
∴ l ⟂ CD
So, l passes through the centre O and is perpendicular to CD, thus it must bisect CD.
Hence, l is the perpendicular bisector of CD.
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