Question

In the given figure, O and O' are centres of two circles, AB//CD//OO′, then which of the following is not true:

Options

• AB = 2 × OO'

• CD = 2 × OO'

• AB = CD

• AB ≠ CD

Answer 1

AB = CD

Explanation:

• Drop perpendiculars from the centers O and O' to the chords AB and CD. The line of centers OO' is perpendicular to both parallel chords AB and CD, and it bisects them at their intersection points with the circles.
• By analyzing the symmetric geometry of intersecting circles where the line of centers runs parallel to the chords, the distance between the chords equals the sum of the radii offsets, but the lengths of chords AB and CD depend on their respective distances from the line of centers. Since the two intersecting circles do not necessarily have equal radii (or even if they do, the chords are segments spanning across the configuration), AB and CD are generally not equal in length.
• Specifically, looking at the options and standard circle theorems for parallel chords in intersecting circles, the statement claiming AB = CD (option iii) is false because chords at different relative positions or in non-identical circles do not have to be equal unless explicitly stated.