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

Answer 1

Hello,
We know the perpendicular from the centre bisects the chord.
Hence, a perpendicular from the center of the circle is the perpendicular bisector of the given chord.
Also, the centre lies on the perpendicular bisector of the chord.
So, above the centre lies on the line L as it is perpendicular bisector of chord AB

Also, AB is parallel to BC
So, angle AGH = angle GHD
(alternate interior angles)
So, angle GHD = 90°
We know that centre lies on line L and L makes and angle of 90 with CD.
Hence, perpendicular from the center bisects the chord.
Hence L bisects CD also.

Please refer the above photograph for the figure and hints.
Hope this will be helping you

WARM REGARDS
Sahil khirwal.

Answer 2

Answer:

Step-by-step explanation:

Given: ab and CD are two chords parallel to each other . Line l is the perpendicular bisector to ab

To prove: line l bisects CD

Proof:

ab is parallel to CD

So, angle AGH = DHG (alternate angles) AGH = DHG = 90°

As we know that line drawn from centre to the circle is perpendicular bisector to the chord

Therefore , l bisects CD

Hence proved