Question

Prove that, if a diameter of a circle bisects two
chords of the circle then those two chords are
parallel to each other.​

Answer 1

If diameter of a circle bisects each of the two chords of a circle. Then the chords are parallel.

Solution:

There are two chords AB and CD , which are bisected by the diameter

We have to prove that AB is parallel to CD

Since, ON bisects CD, therefore ON is perpendicular  to CD

(Perpendicular drawn from centre of the circle to a chord, bisect the chord in equal parts)  

Similarly, OM is perpendicular to AB

To prove that the two chords are parallel we need to show their alternative interior angles are equal

Since, For chord AB and CD , MN act as a transversal and also

Angle AMN = angle MND ( both are 90 degree)

Hence we can say both Chord AB and CD are parallel to each other

Learn more about circles

A diameter PQ of a circle bisect the chord RS at the point O.if PS is parallel to RQ,prove that RS is also a diameter of the circle

Diameter AB of a circle bisect chord PQ. if AQ//BP.prove that chord PQ is also a diameter of a circle

Answer 2

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