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AB and CD are chords such that AB is not parallel to CD. Draw AB and CD's perpendicular bisectors. At what point do perpendicular bisectors of these chords intersect?

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a

Centre of the circle

b

A

c

B

d

D

answer is A.

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Detailed Solution

Given, AB and CD are chords such that AB is not parallel to CD.
We know that perpendicular bisectors of any chord of the circle should pass through the centre.
If two chords are parallel then their perpendicular bisectors coincide with each other.
If two chords are not parallel then their perpendicular bisectors should pass through the centre of the circle.
So, the intersection point of perpendicular bisectors of AB and CD is the centre of the circle.
As a result, option 1 is correct.

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AB and CD are chords such that AB is not parallel to CD. Draw AB and CD's perpendicular bisectors. At what point do perpendicular bisectors of these chords intersect?