If diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.
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Answers
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
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Answer:
answer is in the picture
Step-by-step explanation:
answer is in the picture
